Quantization of gauge fields, graph polynomials and graph cohomology
arXiv:1208.6477 · doi:10.1016/j.aop.2013.04.019
Abstract
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.
44p, many figures, to appear
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Cited by in corpus (17)
- On the analytic computation of massless propagators in dimensional regularization
- Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
- Gravity-Matter Feynman Rules for any Valence
- On the self-consistency of off-shell Slavnov-Taylor identities in QCD
- A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
- Diagrammatic Cancellations and the Gauge Dependence of QED
- The Corolla Polynomial for spontaneously broken Gauge Theories
- Gauge Symmetries and Renormalization
- Log-Expansions from Combinatorial Dyson-Schwinger Equations
- Complexes of marked graphs in gauge theory
- New graph polynomials in parametric QED Feynman integrals
- Algebraic Structures in the Coupling of Gravity to Gauge Theories
- Off-shell Diagrammatics for Quantum Gravity
- Propagator-cancelling scalar fields
- Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically
- Decomposing Feynman rules
- The signed permutation group on Feynman graphs