New Algorithm for Tensor Calculation in Field Theories

TL;DR

This paper introduces a novel graph-based algorithm implemented in C for tensor calculations in field theories, focusing on applications in gravity and quantum field invariants.

Contribution

It presents a new tensor contraction algorithm utilizing graph topology, specifically designed for classical and quantum gravity calculations.

Findings

Successfully computed tensor invariants like $R_{mnls}R^{mnls}$

Demonstrated application to Weyl anomaly calculations

Provided a C-program implementation for tensor contractions

Abstract

Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a special interest. Examples of the leading order calculation of some general invariants such as $R_{\mn\ls}R^{\mn\ls}$ are given. Application to Weyl anomaly calculation is commented.