Do we need Feynman diagrams for higher order perturbation theory?

Physics Letters B (Impact Factor: 6.13). 02/2012; 713(3). DOI: 10.1016/j.physletb.2012.05.047
Source: arXiv


We compute the two and three loop corrections to the beta function for
Yang-Mills theories in the background gauge field method and using the
background gauge field as the only source. The calculations are based on the
separation of the one loop effective potential into zero and positive modes and
are entirely analytical. No two or three loop Feynman diagrams are considered
in the process.

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