tag:blogger.com,1999:blog-10614348.post1747213388414009808..comments2023-01-19T00:50:01.428-08:00Comments on TGD diary: Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds"Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-10614348.post-20836238252549813292014-01-14T05:44:21.391-08:002014-01-14T05:44:21.391-08:00
This is more complicated.
One must distinguish...<br />This is more complicated. <br /><br />One must distinguish between fundamental spinor fields and those used to described various particles. Fundamental spinor fields appear in modified Dirac action: all modes expect right handed neutrino are localised at 2-D string world sheets.<br /><br />The spinor fields that we assign with particles correspond to *imbedding space* spinor fields assignable to cm degrees of freedom of 3-surfaces. This means effective replacement of particle with its cm. This gives QFT description<br />which I believe relies on twistor amplitudes. <br /><br /><br />In string models the situation is exactly the same: the microscopic string level and observable target space level. Also in string models the spinors assigned to physical particles are distinct from those associated with string world sheets. What we observe is not directly the spinors at space-time sheets but something which involves a lot of integration over degrees of freedom which we cannot observe.<br /><br />The large Planck constant can be assigned with any particle: I would not assign it to induced spinor field but to topology of space-time sheet. h_eff=nh, n=n1_n_2 corresponds to n_1- resp. n_2-sheeted coverings of M^4 and CP_2 by space-time sheet. The topology of space-time sheets manifests itself in this manner although otherwise 3-surface representing particle is replaced with its cm. And do not forget that we have always quantum superpositions of surfaces!<br /><br /> Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-22098003076023600922014-01-14T05:19:33.568-08:002014-01-14T05:19:33.568-08:00Dear Matti,
Thanks. as i understand, classical sp...Dear Matti,<br /><br />Thanks. as i understand, classical spinor field are the limit of Second quantised induced spinor field when 3-surfaces replaced with points.<br />also induced kahler field are the limit of kahler field of WCW when the 3-surfaces replaced with points.<br /><br />induced spinor connection of CP2 to macroscopic objects have large Planck constants that we can not observe any electroweak field at this level? <br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-87222663318731027282014-01-14T04:18:04.812-08:002014-01-14T04:18:04.812-08:00Dear Hamed,
I would say that geometry - space-ti...<br /><br />Dear Hamed, <br /><br />I would say that geometry - space-time as surface - is the fundamental. When you know<br />this surface you can deduce various classical fields - induced K\"abler form (Kahler field), electroweak gauge fields, color gauge field, gravitational field as induced metric.<br /><br /> Second quantised induced spinor field whose components other than right-handed neutrino are localised at 2-D string world sheets and they bring in fermions and representation of particles<br /> as field quanta. Gauge bosons and gravitons emerge from fermion antifermion pairs at<br /> wormhole throats. WCW spinor field represents fermion Fock states as functional of 3-surface.<br /> <br /><br />Modified Dirac action and Kahler action are closely related and consistency for the modified Dirac<br />action based on Kahler action requires extremals of Kahler action. <br /><br />One can of course wonder whether one could reduce the dynamics to that for modified Dirac action. For years ago I proposed that Dirac determinant could indeed give rise to Kahler action. I ended up with Riemann Zeta.<br /><br />Naively one expects that the determinant reduces to a product of sub-determinants associated with string world sheets. Their number is in principle infinite: one for each point of partonic 2-surface unless finite measurement resolution somehow makes it finite. <br /><br />How to define this product? Does one take only product over sub-determinants associated with finite number of braid strands serving as ends of allow string world sheets. What principle would fix which string world sheets are allow? Or does one try to define the determinant as product over sub-determinants for a continuum of points of partonic 2-surface? This kind of situation is of course encountered also in QFT so that one might be able to consider logarithm of determinant defined as continuous integral over contributions from different sheets. <br /><br /><br />As I see it, there is no difference between classical and quantum views about particle in TGD framework. Particle has as geometric correlate space-time sheet or to be precise- double structure forming at least double covering of M^4 locally since boundaries are not allowed. Wormhole throats connecting the sheets are building bricks of particle. This double sheet can be glued by wormhole contacts (not carrying monopole flux through them) to large space-time sheet. Quantum description introduces second quantized spinor modes and quantum superpositions of space-time sheets but it does not make particle point.<br /><br />One can of course idealise that situation and this is done at QFT limit where twistorial amplitudes<br />functionally integrate over all the details and effectively only cm degrees of freedom are left in consideration in case of light (originally massless particles).Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-65466652420350568332014-01-14T03:20:18.161-08:002014-01-14T03:20:18.161-08:00Dear Matti,
Thanks for the last answer and the ne...Dear Matti,<br /><br />Thanks for the last answer and the new postings.<br /><br />see is there any misunderstanding?<br />In classical TGD, one can assign to a macroscopic object(for example a system of gas) both classical kahler field and classical spinor field at the same time. information of distributions of particles speeds in the gas is encoded to classical spinor field. <br />and information of geometrical structures of the space-time sheet of the system of gas is encoded to induced kahler field and induced metric.<br />one can ask about action principle for both of the fields(kahler field and spinor field). determining one of them is enough to determine another one. <br /><br />in classical TGD, particles glued to the larger space time but in quantum TGD this is not the correct. in quantum TGD particles are points of larger space time sheet. hence in quantum TGD nothing is glued to another.<br /> <br /><br />suppose that one say also in classical world, particles are points of larger space time and nothing glued to the larger space time.<br />does the picture make sense?Anonymousnoreply@blogger.com