Solving Linear Tensor Equations II: Including Parity Odd Terms in 4-dimensions

2021/12/15 by Damianos Iosifidis, Iosifidis, Damianos
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.2112.07975

8 pages, no figures

arxiv created 2021/12/15 · arxiv updated 2021/12/16

Abstract

In this letter, focusing in 4-dimensions, we extend our previous results of solving linear tensor equations. In particular, we consider a 30 parameter linear tensor equation for the unknown tensor components N_αμν in terms of the known (sources) components B_αμν. Our extension now consists in including also the parity even linear terms in N_αμν (and the associated traces) formed by contracting the latter with the 4-dimensional Levi-Civita pseudo-tensor. Assuming a generic non-degeneracy condition and following a step by step procedure we show how one can solve explicitly for the unknown tensor field components N_αμν and consequently derive its unique and exact solution in terms of the components B_αμν.

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