Using SimTeEx to simplify polynomial expressions with tensors

2024/12/18 by Fonseca, Renato M. · 1 citation
#FOS: Computer and information sciences #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2412.14390

Abstract

Computations with tensors are ubiquitous in fundamental physics, and so is the usage of Einstein's dummy index convention for the contraction of indices. For instance, T_iaU_aj is readily recognized as the same as T_ibU_bj, but a computer does not know that T[i,a]U[a,j] is equal to T[i,b]U[b,j]. Furthermore, tensors may have symmetries which can be used to simply expressions: if U_ij is antisymmetric, then αT_iaU_aj+βT_ibU_jb=(α-β)T_iaU_aj. The fact that tensors can have elaborate symmetries, together with the problem of dummy indices, makes it complicated to simplify polynomial expressions with tensors. In this work I will present an algorithm for doing so, which was implemented in the Mathematica package SimTeEx (Simplify Tensor Expressions). It can handle any kind of tensor symmetry.

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• Two-loop renormalization of general bosonic effective field theories

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