## Sunday, September 16, 2012

### What about the relationship of gravitational Planck constant to ordinary Planck constant?

Gravitational Planck constant is given by the expression hbargr= GMm/v0, where v0<1 has interpretation as velocity parameter in the units c=1. Can one interpret also hbargr as effective value of Planck constant so that its values would correspond to multifurcation with a gigantic number of sheets. This does not look reasonable.

Could one imagine any other interpretation for hbargr? Could the two Planck constants correspond to inertial and gravitational dichotomy for four-momenta making sense also for angular momentum identified as a four-vector? Could gravitational angular momentum and the momentum associated with the flux tubes mediating gravitational interaction be quantized in units of hbargr naturally?

1. Gravitational four-momentum can be defined as a projection of the M4-four-momentum to space-time surface. It's length can be naturally defined by the effective metric gαβeff defined by the anticommutators of the modified gamma matrices. Gravitational four-momentum appears as a measurement interaction term in the modified Dirac action and can be restricted to the space-like boundaries of the space-time surface at the ends of CD and to the light-like orbits of the wormhole throats and which induced 4- metric is effectively 3-dimensional.

2. At the string world sheets and partonic 2-surfaces the effective metric degenerates to 2-D one. At the ends of braid strands representing their intersection, the metric is effectively 4-D. Just for definiteness assume that the effective metric is proportional to the M4 metric or rather - to its M2 projection: geffkl= K2mkl.

One can express the length squared for momentum at the flux tubes mediating the gravitational interaction between massive objects with masses M and m as

gαβeff pαpβ= gαβeffαhkβhl pkpl == geffkl pkpl = n2hbar2/L2 .

Here L would correspond to the length of the flux tube mediating gravitational interaction and pk would be the momentum flowing in that flux tube. geffkl= K2mkl would give

p2= n2hbar2/K2L2 .

hbargr could be identifed in this simplified situation as hbargr= hbar/K.

3. Nottale's proposal requires K= GMm/v0 for the space-time sheets mediating gravitational interacting between massive objects with masses M and m. This gives the estimate

pgr =[GMm/v0] 1/L .

For v0=1 this is of the same order of magnitude as the exchanged momentum if gravitational potential gives estimate for its magnitude. v0 is of same order of magnitude as the rotation velocity of planet around Sun so that the reduction of v0 to v0≈ 2-11 in the case of inner planets does not mean that the propagation velocity of gravitons is reduced.

4. Nottale's formula requires that the order of magnitude for the components of the energy momentum tensor at the ends of braid strands at partonic 2-surface should have value GMm/v0. Einstein's equations T= κ G+Λ g give a further constraint. For the vacuum solutions of Einstein's equations with a vanishing cosmological constant the value of hgr approaches infinity. At the flux tubes mediating gravitational interaction one expects T to be proportional to the factor GMm simply because they mediate the gravitational interaction.

5. One can consider similar equation for gravitational angular momentum:

gαβeff LαLβ= geffkl LkLl = l(l+1)hbar2 .

This would give under the same simplifying assumptions

L2= l(l+1)hbar2/K2.

This would justify the Bohr quantization rule for the angular momentum used in the Bohr quantization of planetary orbits.

Maybe the proposed connection might make sense in some more refined formulation. In particular the proportionality between mkleff= Kmkl could make sense as a quantum average. Also the fact, that the constant v0 varies, could be understood from the dynamical character of mkleff.

At 12:44 AM,  ◘Fractality◘ said...

Hallucinations Caused By Lightning:

http://mindhacks.com/2012/09/12/hallucinations-caused-by-lightning/

At 6:36 AM,  Momentum Formula said...

It has been proven the existence of plancks constant but how it was founded ?If we solve momentum and gravitational problems we use this constant.

At 8:33 AM,  Ulla said...

There are an enormous number of particles predicted by the SM – so far with considerable accuracy. There are also a host of composite particles containing two or three quarks. However, within the SM the lightest boson heavier than the electron (0.511 MeV energy) is a pion having a mass of 135 MeV. Further, there appears no source within the SM from whence a new boson with a mass of 38 MeV might appear.

A true physicist is more excited by evidence that cherished ideas are to some degree wrong than by evidence that reconfirms them. Therefore, should the observation and confirmation of the E(38) boson stand the test of time, a search for how to expand or correct the Standard Model
http://www.gizmag.com/standard-model-particle-physics-unexpected-particle/23897/

http://arxiv.org/abs/1208.3829

At 8:45 AM,  ThePeSla said...

Matti,

I have looked lately at a few of the bloggers I follow whom seem to have ideas that on the face of it appears as a theory of everything if we dare view such claims from some view of deeper foundations- well, we all seem to come closer and how we react to science news to incorporate some discovery after the fact shows a lot toward how sound our theories are.

This is quite a golden age for cosmic speculations. I try to understand more these systems in their alien languages or algebras. So my post today is a little more down to earth in the space structures- and closer I think to understanding your particular views on say the idea of wormholes.

I think it addresses the issue you raise here today rather well on this hierarchy of things like the Planck constant etc... Of course it is a convention for to answer fractality's statement we could stick to non quantum views just as well to derive things like the orbits of electrons- it seems to have wiggle room as a matter of taste or perception... and yes you are among us seeking unification which as statistics can be viewed as some sort of averaging to achieve- but let us not get too rigid.

So do we understand the concepts or have to adjust to our quite isolated and separated but similar perspectives if indeed we can show if some view such as a unified physics is possible- or dare to think so really.

All the talk about Nobel Prizes when there is a forest of them, I mean I would be hard pressed to award it in the usual way and to whom- we just have gone to a new phase of understanding.

Also, Ulla has a most interest link on double lines of magnetic forces on her facebook page- another area recently published that if I can better understand it seems to talk about things you and I and others saw long ago.

Keep the faith while we still live and survive at least, your light like some sentient being to see a single photon assures some star from billions of years ago now exists... the world and I have noted your contribution.

L. Edgar Otto The PeSla

At 11:59 PM,  Ulla said...

PeSla,
.. the world and I have noted your contribution.... most modest :)

All the links I give here support in one or the other way TGD. I have no other good place to give them than here, although mostly out of topic, and considering things we see as self-evident. But a consolidation of TGD need all links it can ever have. Mine is just a small contribution, and Matti said I am too old for this. I just do what i can do. Most of all I would want to write a book about this all. But my situation is a bit difficult.

It seems to me that also mainstream is coming closer to these ideas. But as I also told Hamed, I must first learn to see the tree, before I can handle its branches. FB is a good place to see the tree, I think. All sorts of ideas florishing. I have some interesting groups there.

At 2:44 AM,  Matti Pitkanen said...

To Ulla:

Nice to hear that some people take the possibility that E(38) could exist. This does not mean that one should believe it it.

To my view the numerous anomalies usually forgotten all relate to some profound distinctions between TGD and standard approach. Fractality is certainly one of the most important of these distinctions since it prediction scale versions of what we know as standard model physics. New space concept too is very rich source of new phenomena.

P.S. Sorry for slow responses. Some health problems

At 4:33 AM,  Ulla said...

Oh, sorry to hear that. Hope it is not because of me?

At 4:36 AM,  Ulla said...

They talk about the pionlike state, the only one possible.

At 4:44 AM,  Ulla said...

My dad is today controling his heart and kidney functions. They plan to give him a pacemaker, and it would be much better. Maybe something for you too?
Sometimes the pacemaker does not work, but mostly it does. It would give a much better quality of life. You know I am nobody advertising medical invections generally, but sometimes they are the better choise. Take care.

At 12:18 PM,  hamed said...

Dear Matti,

I saw the definition of holonomy group at Wikipedia. I understand it as follow: Holonomy group of the connection ∇ based at a point x in M is the subgroup of general linear group of the tangent vector space at the point and consisting of all parallel transport maps coming from loops based at x.
If I understand correct, it is not different for the holonomy group if we replace the tangent vector space by a tangent spinor space.
You noted that holonomy group of CP2 is U(2) that is electroweak gauge group.
I don’t understand relation between holonomy group and gauge group. In really in the definition of holonomy group, I don’t see anything relate to gauge potential. Please help me to understand it.

At 7:34 PM,  hamed said...

Dear Matti,
If because of the health problems it is hard for you to answer, i can wait for that.

At 11:07 PM,  matti Pitkanen said...

Dear Hamed,

I feel now somewhat better. I even replied to your question but did not notice that it was sent via blog rather than directly. So that it you have probably not received the response. I forgot also to store the message which I do usually. I will try again later.

At 11:12 PM,  Matti Pitkanen said...

To Ulla:

It seems that your father and me has similar problems. Now I had virus infection and it caused also arhythmia and this in turn exhaustion and breathlessness. In however think that pacemaker is not yet topical. Time will show.

At 11:26 PM,  hamed said...

Dear Matti,
No i didn't receive it. I am very thankful if you write it again to me when you have enough time to writing.

At 11:45 PM,  Matti Pitkanen said...

Dear Hamed,

a new trial;-). If the text loooks incoherent, it probably is incoherent but I have an excuse;-). Your interpretation of holonomy group is quite correct.

The theory of vector bundles is extremely general and one any linear space is in principle. Linear bundle is special kind of manifold obtained by replacing the Cartesian product MxV, V linear space with its local version decomposing pieces of MxV glued together by identification maps which are gauge transformations for a physicist: that is union of finite number of repions MxV and identified in the patching regions by an element g(x) of structure group G acting in the linear space V.

Parallel translation of vectors of V and connection performing it can be defined in extremely general and purely geometrically in this space but phycisists preferred to use the concrete definition in terms of gauge potentials definition the connection coefficients defining as gauge potentials A_mu defined as 1-forms having values in the Lie algebra of the structure group. Riemann connection looks somewhat different but in vielbein basis it also reduces to 1-form.

The tangent bundle of sphere is good concrete example about non-trivial vector bundle and I suggest that you try to understand it as application of general definitions.

The structure group of spinor connection is covering group of that for vielbein connection. For instance, for E^3 the structure group is SO(3) for tangent and its double covering SU(2) for spinor bundle. These groups are therefore not the same in general. In case of CP_2 the structure group is SO(4)=SU2_LxSU(2)_R and therefore its own covering group.

In the case of CP_2 however the topology of CP_2 implies that ordinary spinor connection does not exist. The problem is that for a closed curve the gauge transforms representing changes of the coordinate patch do not sum up to unit transformation but a phase multiplication. The problem can be overcome by coupling spinors to an odd multiple of Kahler gauge potential. The structure group gets an additional U(1) factor.

Holonomy group is subgroup structure group and in case of CP_2 spinor connection contains SU(2)_L algebra, neutral part of SU(2)_R and U(1) due to the addition of coupling to Kahler gauge potential. One can imagine that it is obtained by studying holonomies over infinitesimal quadrilateral paths in various 2-planes. The holonomy element is by definition exp(iA_mudx^mu) at this limit and by expanding one obtains 1+iPhi, Phi= F_munudx^udx^nu, the magnetic flux over the infinitesimal quadrilateral. By dividing with the area of quadrilateral one obtains an element of Lie algebra of holonomy group and by taking the commutators of these normalized magnetic fluxes one obtains the Lie algebra of holonomy group.

The identification of the holonomy group of spinor connection as gauge group is a separate postulate suggested to realize the geometrization of the electroweak interactions. The motivation is that the coupling structure is same as for electroweak gauge potential. There is also the fact that electroweak symmetry breaking is coded by CP_2 geometry at classical level. What is of special importancen is that the U(1) facor of Spin_c is absolutely necessary physically. If one assumes that S is symmetric space then the presence of this factor forces CP_2.

At 12:12 AM,  hamed said...

At 12:57 PM,  hamed said...

I started to study the chapter” CONNECTIONS ON FIBRE BUNDLES” in the book of Nakahara “Geometry topology and physics”. It contains holonomy group and physical examples too. I try to finish it in the days.
Now I have a question in quantum TGD:
In Standard QM the state of a system is represented by a vector in infinite dimensional complex Hilbert space and in quantum TGD, state of a system is represented by a vector in infinite dimensional Clifford algebra or HFF2. In really, every 3-surface is represented by a vector in the HFF2. The space of states is at light-like boundaries of the causal diamond (CD).
The state function (or M matrix) is collapsed to zero modes (Classical degrees of freedom) in each quantum jump. Why do you name “zero mode” for classical degrees of freedom? Union of infinite-dimensional symmetric spaces labeled by zero modes. Therefore in each quantum jump, state function is localized to some symmetric space. I don’t understand any relation between classical degrees of freedom and zero modes?
In standard QM, when we measure a quantity like the position of a particle, after the measurement, the state function collapse to the eigenstate |^2. What is this principle of QM in translating to quantum TGD? <X| is a classical degree of freedom?

At 11:28 PM,  Matti Pitkanen said...

Dear Hamed,

thank you for excellent and very stimulating questions. I thought that I should post it first as a background and answer your questions after that.

a) Also in TGD state space is basically Hilbert space. But Hilbert space as such is extremely general notion. Only when one gives it additional structure and concrete realization one obtains the space of quantum states.

b) In TGD this structure comes when one identifies states of Hilbert space as WCW spinor fields. The analogy with ordinary spinor field helps to understand what they are.

I try to explain by comparison with QFT.

1. What happens in ordinary QFT in fixed space-time?

Ordinary spinor is attached to an space-time point and there are 2^D/2 dimensional space of spin degrees of freedom. Spinor field attaches spinor to every point of space-time in a continuous/smooth manner. Spinor fields satisfying Dirac equation define in Euclidian metric a Hilbert space with a unitary inner product. In Minkowskian case this does not work and one must introduce second quantization and Fock space to get unitary inner product. This brings in what is essentially basic realization of HFF2 as allowed operators acting in this Fock space. It is operator algebra rather than state space which is HFF2 but they are of course closely related.

2. What happens TGD where one has quantum superpositions of space-times?

a) First guess: space-time point is replaced with 3-surface: point to 3-surface representing particle. WCW spinors are fermionic Fock states at this surface. WCW spinor fields are Fock state as a functional of 3-surface. Inner product Fock space inner product plus functional integral over 3-surfaces. One could speak of quantum multiverse. Not single space-time but quantum superposition of them. This quantum multiverse character is something new as compared to QFT.

b) Second guess forced by ZEO, by geometrization of Feynman diagrams, etc.

*3-surfaces are actually not connected 3-surfaces. They are collections of components at both ends of CD and connected to single connected structure by 4-surface. This is like incoming and outcoming particles in connected Feynman diagrams. Lines as regions of Euclidian signature or the 3-D boundaries between Minkowskian and Euclidian signature.

*Spinors(!!) are defined now by the fermionic Fock space of second quantized induced spinor fields at these 3-surfaced and by holography at 4-surface. This fermionic Fock space is assigned to all multicomponent 3-surfaces defined in this manner and WCW spinor fields are defined as in the first guess. . This brings integration over WCW to the inner product.

c) Third, even more improved guess motivated by the solution ansatz for preferred extremals and for modified Dirac equation giving connection with string models.

*The general solution ansatz restricts all spinor components but right-handed neutrino to string world sheets and partonic 2-surfaces: effective 2-dimensionality. String world sheets and partonic 2-surfaces intersect at the common ends of light-like and space-like braids at ends of CD and at along wormhole throat orbits so that effectively discretization occurs. This fermionic Fock space replaces the Fock space of ordinary second quantization.

To sum up, the core idea is expressed in item 1. The rest is just gradual detailing and refining.

To be continued....

At 11:44 PM,  matti Pitkanen said...

Dear Hamed,

a) You say: "In Standard QM the state of a system is represented by a vector in infinite dimensional complex Hilbert space and in quantum TGD, state of a system is represented by a vector in infinite dimensional Clifford algebra or HFF2. "

My comment: To be precise, HFF2 belongs to the algebra of operators acting in fermionic Hilbert space. As linear space this algebra can made itself Hilbert space. The technical details related to the topology go over my head. One can say that vector in HFF creates Hilbert state from vermionic vacuum, Dirac sea. One can normal order this operator so that all creation operators act first so that this vector seems also unique. In *this sense* the Hilbert space states and operators creating them are in one-one correspondence.

b) You say: "In really, every 3-surface is represented by a vector in the HFF2". This is not quite true. It is the Clifford algebra of fermionic Fock space which has HFF2 property but also a lot of other physical structure. 3-surface cannot be seen as a vector in HFF2: for instance, WCW is strongly non-linear object (union of symmetric spaces) and its points cannot be added as those of HFF2. 3-surface is generalization of point appearing as an argument of spinor field. This is the good intuitive starting point. I tried to clarify this issues in the first response.

c) You say: "The state function (or M matrix) is collapsed to zero modes (Classical degrees of freedom) in each quantum jump. Why do you name “zero mode” for classical degrees of freedom? Union of infinite-dimensional symmetric spaces labeled by zero modes. Therefore in each quantum jump, state function is localized to some symmetric space. I don’t understand any relation between classical degrees of freedom and zero modes?"

My comment: Here there is a slight mis-understanding. I would not say that state function is collapsed to zero modes. WCW is (as I conjecture!) a union of symmetric spaces labelled by zero modes. I try to explain.

*Zero modes are fixed when the induced Kahler form is fixed in 4-D tangent spaces of partonic 2-surfaces (and maybe also of 4-D tangent space of string world sheets). This pattern of values of induced Kahler form defines "purely classical degrees of freedom", zero modes. They do not contribute to WCW line element.

*Quantum fluctuating degrees of freedom correspond degrees of freedom of WCW contributing to WCW Kahler metric. The natural conjecture is that they are parametrized by the symplectic group of delta CDxCP_2 leaving induced Kahler form invariant (and therefore zero modes) and acting as isometries of WCW.

*This symplectic group - or presumably some coset space of it - becomes the space of quantum degrees of freedom. This space would be an infinite-D symmetric space. And each pattern of the induced Kahler form identified in proposed manner would correspond to one almost copy of this kind of symplectic space (Kahler metric could contain a conformal factor depending on zero modes).

*Zero mode part of the state can entangle with quantum fluctuating part. Measurement apparatus would indeed create a correlation between quantum fluctuating parts of the state and zero modes. For instance electron's different spin directions would correspond to slightly different patters of induced Kahler form at tangent spaces of these 2-surfaces. In state function reduction a localization in zero modes occurs and leads to a selection of one particular outcome for quantum state. Or the other way around! It is difficult so ay which causes which.

*Localization occurs *only* in zero modes!! In quantum fluctuating degrees of freedom one has still delocalization. This is almost synonymous for being quantum fluctuating! These degrees of freedom are analogous to vibrational degrees of string.

At 1:52 AM,  matti Pitkanen said...

Dear Hamed,

still a little comment.

*WCW is not HFF of type II as I noticed since it is not linear space nor algebra. But the group algebra associated with infinite discrete subgroups of the symplectc group defining quantum fluctuating degrees of freedom probably are!. What is so nice that these group algebras are discrete analogs for wave functions in WCW: orbital degrees of freedom of WCW spinor field.

* WCW spinors define a canonical HFF II_1 so that both WCW-spinorial (fermionic) and WCW "orbital" degrees of freedom are HFFs. The Interpretation is as analog of supersymmetry at WCW level.

I try to explain.

a) In nonzero modes WCW is symplectic group of delta M^4_+xCP_2 (call it Sympl) which reduces to the analog of Kac-Moody group associated with S^2xCP_2, where S^2 is radius constant sphere of light-cone boundary and z is replaced with radial coordinate.

Finite measurement resolution, which seems to be coded already in the structure of preferred extremals and of solutions of modified Dirac, suggests strongly that this symplectic group is replaced by its discrete subgroup or coset space. What this group is depends on measurement resolution defined by the cutoffs.

b) Why these discrete subgroups of Sympl would lead naturally to HFFs of type II?

*There is a very general result stating that group algebra of enumerable discrete group which has infinite conjugacy classes and is amenable so that its regular representation in group algebra decomposes to all unitary irreducibles is HFF of type II. See

http://en.wikipedia.org/wiki/Hyperfinite_type_II_factor.

*These group algebras associated these discrete groups would thus be HFFs of type II_1 and their inclusions would define finite measurement resolution: included algebra would create rays of state space not distinguishable experimentally. The inclusion would be characterized by the inclusion of the lattice defined by the generators of included algebra by linearity. One would have inclusion of this lattice to a lattice associated with a larger discrete group. Inclusions of lattices are however known to give rise to quasicrystals (Penrose tilings are basic example), which define basic non-commutative structures. This is indeed what one expects since the dimension of the coset space defined by inclusion is algebraic number rather than integer.

An interesting question remains: What about zero modes? They are certainly discretized too. One might hope that one-one correlation between zero modes (classical variables) and quantum fluctuating degrees of freedom suggested by quantum measurement theory allows to effectively eliminate them.

At 6:05 AM,  hamed said...

Dear Matti,

Thanks a lot, sorry for delaying. I could not access to internet in my free times.
some questions in bellow sentences:
“Zero modes are fixed when the induced Kahler form is fixed in 4-D tangent spaces of partonic 2-surfaces (and maybe also of 4-D tangent space of string world sheets). This pattern of values of induced Kahler form defines "purely classical degrees of freedom", zero modes.”
At “induced Kahler form is fixed in 4-D tangent spaces of partonic 2-surfaces” it is something dimly for me. As I learned in the past, induced kahler form is component projection of Kahler form of CP2 on the spacetime surface. This was in classical TGD but In Quantum TGD, is it induced on every spacetime surface in quantum superposition of them?
If it is correct, I follow another question. When you say it can be fixed in 4-D tangent spaces of partonic 2-surfaces, I understand from this sentence: The induced kahler form on the spacetime surfaces is in really in the 4-D tangent spaces of somespace and not on the spacetime surfaces themselves. And if it is fixed to partonic 2-surfaces, this pattern of values of induced Kahler form defines zero modes? I think my last sentences are very incorrect:).

At 8:15 AM,  matti Pitkanen said...

Dear Hamed,

Thank you for questions. I really enjoy these discussions since they allow me to retrieve the basic ideas in more detail. I hope you can get the gist of arguments.

Your question: "As I learned in the past, induced kahler form is component projection of Kahler form of CP2 on the spacetime surface. This was in classical TGD but In Quantum TGD, is it induced on every spacetime surface in quantum superposition of them?"

My answer: You are right. In quantum TGD and classical TGD the situation is exactly same: classical physics efined by preferred extemals is an exact part of quantum physics in TGD since WCW metric assigns to 3-surface space-time surface as a kind of Bohr orbit.

As I explained, 3-surface corresponds to ends of space-time surface at boundaries of CD or orbits of partonic 2-surfaces (wormhole throat orbits at which signature of the induced metric changes). Strong form of holography requires that it is actually the intersections of space-like ends and wormhole throat orbits defining partonic 2-surfaces plus the 4-D tangent space of them which codes for physics.

Your question: " In quantum superposition one has zero modes for each surface is superposition and a natural postulate would be that quantum fluctuating part of state correlates with zero mode part. What this exactly means is not quite clear."

My answer: The point is that zero modes represent classical variables: "position of the pointer of measurement apparatus" is the poetic metaphor for this. When state function reduction selecting one particular state in superposition of states occurs, it must fix the pointer to corresponding position. This requires correlation- that is entanglement and thus sum SUM c_m(N) |m> |N> where |m> corresponds to zero mode state and |N> to quantum fluctuating state. Zero modes are here symplectic invariants and complete localization is suggestive.

To be continued....

At 8:18 AM,  matti Pitkanen said...

Dear Hamed,

I have been retrieving what I have said about zero modes and realized that my loose claim that all zero modes are symplectic invariants is wrong.

The fluxes of induced CP_2 Kahler form and delta M^4_+ Kahler form over regions of partonic surfaces (Kahler magnetic fluxes) are certainly zero modes and also symplectic invariants - therefore classical variables.

There are however also zero modes which do not seem to correspond to classical variables since they are not symplectic invariants.

a) The point is that the symplectic group of delta M^4_+xCP_2 is generated by Hamiltonians. They are products of three factors: S^2 Hamiltonian (r_M constant sphere of light-cone boundary parametrize by theta, phi) assumed to have well-defined SO(3) quantum numbers, CP_2 Hamiltonian with well defined color quantum numbers, and power r_M^n. r_M is in the same role as powers of z in the definition of Kac-Moody algebra and one can indeed identify the algebra as a generalization of KM algebra with the finite-D Lie-algebra replaced with symplectic algebra of S^2xCP_2. *Only* the generators with n different from 0 contribute to the WCW metric. So that zero modes are in question. But are they classical variables?

b) What is then the role of n=0 sector: the symplectic algebra of S^2xCP_2. One can assign to this sub-algebra of Sympl hierarchy symplectic measures obtained by wedge powers of WCW symplectic form and restricted to finite-D symplectic manifolds and one would have inner product. Does the finite dimension of the symplectic sub-manifold define part of measurement resolution. Wave function in this manifold instead of complete localization.

In this sector one does not have metric measure but one has a hierarchy of symplectic measures defined by exterior powers of symplectic form restricted to finite-D symplectic sub-manifolds. This is enough for inner product.

c) Do these zero modes deserve interpretation as classical degrees of freedom? The following argument suggests that this is not the case.

* In Kac-Moody analogy they would correspond to n=0 KM generators defining ordinary finite-D Lie algebra and ground states of Kac-Moody representations transform according to them. Perhaps zero modes are not in question but ground states of the representations of full symplectic group analogous to KM. For instance, in WCW spinor sector ground states of fermionic KM representations are defined byM^4xCP_2 harmonics for imbedding space spinors: this is assumed in p-adic mass calculations.

*Besides zero modes there are also other parameters such as the conformal moduli of partonic 2-surfaces defining global variables depending only on conformal equivalence class of partonic 2-surface.

To conclude, the structure is really infinitely rich. The magic is that by finite measurement resolution the entire WCW could reduce to an enumerable discrete space, and the theory of HFFs of type II_1 provides general results allowing to gain a lot of understanding about the general architecture!

At 10:17 AM,  ThePeSla said...

Matti,

I have realized the topic here was a question I was going to ask- so you are concerned with that very question. In my late ideas I considered what was meant by this scale question of such analogs to action values (from a more finite perspective) and seem drawn more to the golden ratio where it involves our ideas of primes.

So I have the general feeling that where things show up as in the constant 1/89 or the repeating of digits over so many periods starting with 11 and so on that the key could be in how you have determined (presumably p-adic) these values of which I am not quite sure I fully understand in detail.

That said, in my thoughts of last night I think I found a further generalization of the string and brane like theories.

Gibbs has an interesting post where he has not posted much because the Higgs excitement and the rapid vanishing of new physics ideas now ho hum- well, it seems that you and I, as stressful as it may be in this world of absurd implementing of technology and the resource of all our minds, we have not lost this excitement!

I am not sure the future as being on line is good enough to replace one on one dialog in person- but open source (see Lubos today) for particle physicists.

I may take a break- music and stuff unless something spectacular occurs to me awake or in some dream space. Yet, it is most certain that individual contributions such as yours may leave a long shadow- a book on your life I would find essential reading by the way.

I saw on the tele that Finns and Russian have a tendency for high blood pressure- do you by chance have migranes as did my string theory friend who graciously talked with me when he was feeling well while teaching at the university and I think had similar problems (all of which if people cared our esoteric theories would cure and touch them deeply if they cared... especially those in the power to write the agenda of science.

Thoughts shared from a distance:

The PeSla

At 7:05 PM,  matti Pitkanen said...

Dear Pesla,

I do not suffer migraine in the usual sense. Only if I have worked too long at terminal, a kind of blinking colorful hole can appear in the visual field. It actually then goes to auditory field: I cannot understand speech from ratio and then fades. It is certainly just over overstress. There is no head each or nausea.

At 9:40 PM,  hamed said...

So thanks dear Matti, i must to review on my last informations by the new understandings.

Best Wishes for you