Symbolic algebra and renormalization of gauge theories. (English) Zbl 0888.65128
Summary: Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of gauge theories. This scheme is readily implemented using the general purpose package, Mathematica. The techniques discussed are used to calculate renormalization group functions for a non-Abelian \(\text{SU}(m)\) gauge theory with massless fermions in a representation \(R\), in the two-loop approximation, and to simplify some expressions arising in electroweak calculations at the two loop level.
MSC:
| 65Z05 | Applications to the sciences |
| 65Y15 | Packaged methods for numerical algorithms |
| 35Q40 | PDEs in connection with quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 68W30 | Symbolic computation and algebraic computation |
| 81Q40 | Bethe-Salpeter and other integral equations arising in quantum theory |
Keywords:
perturbation theory; quantum field theory; symbolic algebra; Lorentz tensor; Dirac and symmetry group algebra; Feynman integration; Mathematica; renormalization group functions; non-Abelian \(\text{SU}(m)\) gauge theoryReferences:
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