Sunday, November 15, 2009

Is the QFT type description of gravitational interactions possible in TGD framework?

During the last month I have developed a formulation for the super-symmetric QFT limit of quantum TGD based on the generalization of chiral and vector super-fields appropriate for N=∞ supersymmetry. The next question concerns the possibility to describe gravitational interactions using QFT like formalism. The physical picture is following.

  1. In TGD Universe graviton is necessarily a bi-local object and the emission and absorption of graviton are bi-local processess involving two wormhole contacts: a pair of particles rather than single particle emits or absorbs graviton. This is definitely something new and defies a description in terms of QFT limit using point like particles. Graviton like states would be entangled states of vector bosons at both ends of string and propagating collinearly so that gravitation could be regarded as a square of YM interactions in a rather concrete sense.

  2. The connection with strings is via the assignment of wormhole contacts at the ends of a stringy curve. Stringy diagrams would not however describe graviton emission. Rather, a generalization of the vertex of Feynman diagram would be in question in the sense that three string world sheets would be glued together along their 1-dimensional ends in the vertex. This generalizes similar description for gauge interactions using Feynman diagrams. In the microscopic description point like particles are replaced with 2-D partonic surfaces so that in gravitational case one has stringy 3-surfaces at vertices.

This picture provides strong constraints if one wants to describe gravitation using a generalization of QFT type theory.

  1. At QFT limit one can hope a description as a bi-local process using a bi-local generalization of the QFT limit so that stringy degrees of freedom need not be described explicitly. There are hopes about success, since these degrees of freedom have been taken into account in the spectrum of modes of the induced spinor field and reflect themselves as quantum numbers labeling fermionic oscillator operators. Also modified gamma matrices feed information about space-time surface to the theory.

  2. The hypothesis is that a generalization of the super-symmetric QFT limit to its bi-local variant allows to describe the emission and absorption of gravitons. Also now the kinetic part for gravitational action emerges so that only the counterpart of Tαβδ gαβ interaction term appears in the fundamental action.

  3. The idea about gravitation as a square of YM theory generalizes in the sense that graviton is a pair of gauge bosons at the ends of string d and bosonic propagators determine graviton propagator. The fact that bosonic loop is dimensionless implies that IR cutoff defined by the size of largest CD must be actively involved. The requirement of gauge invariance fixes uniquely the form of the bi-local gravitational action. The form is remarkably simple.

  4. A huge number of graviton like states together with their super-partners are predicted (super-symmetry is N=∞ SUSY in the general case!). Most of them are massive. The ordinary graviton must correspond to electroweak gauge group U(1) for which charge is essentially fermion number (quantum counterpart of Kähler gauge potential of CP2). This means that gravitational Weinberg angle vanishes.

I feel it fair to say that the addition of the measurement interaction term to the modified Dirac action has led to a profound understanding of Quantum TGD at mathematical level - consider only the generalization of the super-fields as an example. It remains to be seen how far-reaching the implications are for the more technical understanding of quantum TGD proper.

For more details the interested reader can consult the five-page excerpt Is the QFT type description of gravitational interactions possible? from the new chapter Does the QFT Limit of TGD Have Space-time Super-Symmetry? of the book "Towards M-Matrix".


Frank said...

I had been looking around for theories of everything that took quantum geometrodynamics and cognition into account and came across TGD. Though I believe I understand most of what TGD implies just from reading what you have written, I would like to discuss it more in-depth with you if you ever have the time and energy. Specifically, I would like to hear your input on how your TOE differs from other physicists (such as Tegmark's TOE).

Matti Pitkänen said...

Ok, I am willing to discuss. My email address is

Doug said...

Hi Matti,

With respect to chiral fields, consider chiral media such as that of EE-PhD Akhlesh Lakhtakia [Penn State] who wrote "Beltrami Fields in Chiral Media" in 1994, 535 pages.

Viewable on Google books.

Frank said...

Ok; I emailed you my first set of questions.

Matti Pitkänen said...

Thank you Doug.

The generalization of Beltrami fields to their 4-D variants as Maxwell fields (actually Kahler form projected to space-time surface) with a vanishing Lorentz 4-force appear in the general solution ansatz for field equation of TGD. Since dissipation and 3-force are absent, the interpretation was that they represent space-time correlates for asymptotic self organization patterns.

At that time the interpretation was not quite logical since these solutions should have been the only ones. The addition of measurement interaction term to Kahler action makes this interpretation however completely ok.