Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Remarks on a New Possible Discretization Scheme for Gauge Theories

Remarks on a New Possible Discretization Scheme for Gauge Theories We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Theoretical Physics Springer Journals

Remarks on a New Possible Discretization Scheme for Gauge Theories

Download PDF
10 pages

Loading next page...
 
/lp/springer_journal/remarks-on-a-new-possible-discretization-scheme-for-gauge-theories-YCcezMmOXq
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Physics, general; Quantum Physics; Elementary Particles, Quantum Field Theory; Theoretical, Mathematical and Computational Physics
ISSN
0020-7748
eISSN
1572-9575
DOI
10.1007/s10773-018-3733-3
Publisher site
See Article on Publisher Site

Abstract

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Journal

International Journal of Theoretical Physics – Springer Journals

Published: Mar 28, 2018

References

  • Construction of convergent simplicial approximations of quantum fileds on Riemannian manifolds
    Albeverio, S; Zegarlinski, B
  • The Wilson loop observables of Chern-Simons theory on $\mathbb {R}^{3}$ℝ3 in axial gauge
    Hahn, A
  • Vertex functions of Coulomb gauge Yang–Mills theory
    Huber, M; Campagnari, D; Reinhardt, H
  • The mean value for infinite volume measures, infinite products and heuristic infinite dimensional Lebesgue measures
    Magnot, J-P
  • Yang-mills in axial gauge
    Reinhardt, H
  • Covariant loop quantum gravity
    Rovelli, C; Vittodo, F
  • A geometric discretisation scheme applied to the Abelian Chern-Simons theory
    Sen, S; Sen, S; Sexton, JC; Adams, DH
  • Geometric Integration Theory
    Whitney, H