Gauge Theory; Parallelism; Kleinert; Wong Equations (11)

Below: A few notations to indicate topics covered. Author’s page numbering is ignored, page numbers referenced below are from the scanned PDF documents.**recommend reading in Two Page Scrolling in Adobe, under ‘View”.

Notebook September 2010 – February 2011:

Gauge Theory and Paralellism, Kleinert, Wong Equations: Work is concurrent with Notebook: Wong Equations for Gravitation

  • (p. 33-34) Concerning Kleinert’s proposal:
    • Teleparallel gauge 1 / Einstein-Hilbert gauge 2 ⇨⇨ Unified Theory
      • 1. Presumably one can incorporate symmetric teleparallel gravity into the scheme.
      • 2. Tanimura deduced the curvature (Einstein-Hilbert) formulation of GR from the modified Feynman argument with
  • We have deduced (almost) the equation of motion for a translation gauge theory by taking Iα  =  Pα in the gauge theory approach of Tanimura. We expect to get teleparallel’s EOM.
    • Both of these approaches should be related by Kleinert’s gauge symmetry.
  • Coming at gravity from the non-abelian gauge theory angle often leads to torsion.

(p. 42) Perhaps our gauge-gravity has revealed a way to subsume Riemannian Geometry into the Erlangen Programme once we understand the symmetry meaning, or perhaps the “interpretation” of

  • (p. 75) Poincare’s geometric conventionalism–a revival
    • Teleparallel / Riemannian / Symmetric teleparallel⇒⇨Continuum of possibilities corresponding to gauge choices that correspond to different geometries and different oberservables. c.f. Kleinert

(p. 77) It is a gauge choice whether to blame gravitational effects on local translations or local rotations.

(p. 79) The month of November is continued in the notebook: Wong Equations for Gravitation.

  • (p. 93-94) Let’s examine the possible equivalence of the 3 different formulations of GR
    • Einstein
    • Teleparallel
    • Symmetric Teleparallel
  • In the symmetric teleparallel approach we covariantize the coordinates which may help in passing to a non-commutative algebraic approach.
  • The question of gravitational energy momentum conservation will be solved with the understanding of Noether’s theorem extended to include groupoids.
  • We must do a study of the nature of supersymmetry in these alternative geometriesThese may be a very interesting relation between paralelizability and SUSY. Paralelizability is already very desirable from dynamical (initial value) formulations, and in the construction of canonical frames in the teleparallel theory.
  • It is necessary to provide a Noether’s theorem for groupoids in order to understand gravity!

(p. 100) It’s possible that the necessity of requiring asymptotic isometry group in QFT, which is, by the results of AdS/CFT, what make the string theory/field theory model of gravity background dependent, comes from a long-known property of Quantum Theory: the measuring device must be classical. In order for the measuring device to be ‘classical’ it must exist in an isotropic spacetime. Can this be justified? What is truly required of a classical measuring device?

(p. 108) Tuesday, December 14, 2010 Today we play around with noncommutativity and supersymmetry as a consequence of our gravitational formalism.

(p. 129) What happens if we do ordinary Yang-Mills but allow the structure constants to fluctuate ever so slightly?

(p. 137) Next layer of physical detail: ___”Points” should be big enough to allow an internal angular and linear momentum.

(p. 140) The fundamental statement is that the physics of 2 harmonic oscillators, with spin and angular momentum, confined to the x-y plane, with an external B-field in the z direction is a supersymmetric system.…so, we have spinning particles subject to 2 external forces.

  • (p. 144) On the Question of Background Independence
    • The present formulation of string theory suffers from a defect that may indicate the need for a fundamental rethinking of the program: background dependence.
    • By “background dependence‘ we mean that any theory in which space and time play a role along with other physical entities and when the following obtains:
      • 1. We can cannonically associate a group g to the spacetime irrespective of the state of other physical entities
      • 2. We denote the mathematical structure that is associated with spacetime degrees of freedom: M
      • Typically, when gravitation itself is considered classically (i.e. we are not doing quantum gravity) M is a manifold.
    • We call the pair ( M, g ) the background.
  • The question of background independence is related to the long-standing philosophical argument (c.f. Leibing) that the correct theory of physics must be background independent because space and time are truly relations between the other physical entities appearing in the theory.

(p. 146-147) A Critique of Relationalism. Actually, to be more precise, we think of spacetime to be made up of relationships between particles, not fields. Spacetime is all the relations between localizable entities. In a field theory the excitations that constitute particles are not the fundamental entities in the theoryWe have, at this point to make a distinction between defining spacetime as the set of relations between all possible configurations of particles versus defining spacetime as only relations between measured particles. Do we create spacetime by measuring local quantities?