Physical Sciences and Mathematics Commons^™

For The Dissertation: A Classification Of Tensors In Ecsk Theory, Joshua James Leiter, Charles G. Torre

Physics Student Research

This dissertation presents a Petrov/Plebanski/Segre/Algebraic (PPSA) classification scheme for both the curvature and torsion tensors in Einstein-Cartan-Sciama-Kibble theory (ECSK); additionally the work includes a software package in Maple with computational and PPSA classification tools. Six different solutions are classified using the new software tools developed. We also present a new boundary term for ECSK-NMC scalar theory to ensure Dirichlet boundary conditions. New work completed includes the decomposition of an arbitrary 4th rank tensor under SO (p, q), equivalent SL (2, C) irreducible spinor decompositions of arbitrary 3rd and 4th rank tensors. We provide new proofs that the corresponding spinors are …