Quantization of gauge fields, graph polynomials and graph homology

Kreimer, Dirk; Sars, Matthias; van Suijlekom, Walter D.

doi:10.1016/j.aop.2013.04.019

Quantization of gauge fields, graph polynomials and graph homology

Dirk Kreimer
(
- Humboldt U., Berlin and
- Nijmegen U.
)
,
Matthias Sars
(
- Humboldt U., Berlin and
- Nijmegen U.
)
,
Walter D. van Suijlekom
(
- Humboldt U., Berlin and
- Nijmegen U.
)

Aug, 2012

43 pages

Published in:

Annals Phys. 336 (2013) 180-222

Published: 2013

e-Print:

1208.6477 [hep-th]

DOI:

10.1016/j.aop.2013.04.019

Report number:

MAPHY-AVH-2012-10

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Abstract: (Elsevier)

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.

Note:

44p, many figures, to appear

Gauge theory
Graph homology
Covariant quantization
gauge field theory: quantization
gauge field theory: nonabelian
gauge: covariance
ghost
cohomology
homology
graph theory

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