TITLE:
Fourth Rank Energy-Momentum Tensor
AUTHORS:
Vu B. Ho
KEYWORDS:
Fourth Rank Energy-Momentum Tensor, Riemannian Manifold, Riemann Curvature Tensor, Electromagnetic Field, Dirac Field
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.12,
December
28,
2022
ABSTRACT: In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.