Quantization of gauge fields, graph polynomials and graph homology

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• 作者：Dirk Kreimer ; Matthias Sars ; Walter D. van Suijlekom
• 关键词：Gauge theory ; Graph homology ; Covariant quantization
• 刊名：Annals of Physics
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：336
• 期：Complete
• 页码：180-222
• 全文大小：1278 K

文摘

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at 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.