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Title: Quantization of gauge fields, graph polynomials and graph homology

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
Authors:
 [1] ;  [1] ;  [2]
  1. Humboldt University, 10099 Berlin (Germany)
  2. Radboud University Nijmegen, 6525 AJ Nijmegen (Netherlands)
Publication Date:
OSTI Identifier:
22220778
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 336; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GRAPH THEORY; POLYNOMIALS; QUANTIZATION; REVIEWS; SCALAR FIELDS