Open AccessDerivation of the Symmetric Stress-Energy-Momentum Tensor in Exterior Algebra
Author(s) -
Ivano Colombaro,
Josep Font-Segura,
Alfonso Bahillo
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012050
Subject(s) - multivector , tensor (intrinsic definition) , symmetric tensor , mathematics , tensor contraction , tensor density , stress–energy tensor , cauchy stress tensor , tensor calculus , tensor field , action (physics) , lanczos tensor , infinitesimal , mathematical physics , algebra over a field , pure mathematics , mathematical analysis , physics , exact solutions in general relativity , quantum mechanics , subalgebra , division algebra
We present a derivation of a manifestly symmetric form of the stress-energy-momentum using the mathematical tools of exterior algebra and exterior calculus, bypassing the standard symmetrizations of the canonical tensor. In a generalized flat space-time with arbitrary time and space dimensions, the tensor is found by evaluating the invariance of the action to infinitesimal space-time translations, using Lagrangian densities that are linear combinations of dot products of multivector fields. An interesting coordinate-free expression is provided for the divergence of the tensor, in terms of the interior and exterior derivatives of the multivector fields that form the Lagrangian density. A generalized Leibniz rule, applied to the variation of action, allows to obtain a conservation law for the derived stress-energy-momentum tensor. We finally show an application to the generalized theory of electromagnetism.