Operator-Valued Tensors on Manifolds: A Framework for Field Quantization
Mathematical Physics
2015-01-28 v2 math.MP
Abstract
In this paper we try to prepare a framework for field quantization. To this end, we aim to replace the field of scalars R by self-adjoint elements of a commutative C-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian metrics to operator valued metrics. Then, in this new geometry, some essential concepts of Riemannian geometry such as curvature ten- sor, Levi-Civita connection, Hodge star operator, exterior derivative, divergence,... will be considered.
Cite
@article{arxiv.1501.05065,
title = {Operator-Valued Tensors on Manifolds: A Framework for Field Quantization},
author = {Hassan Feizabadi and Nasser Boroojerdian},
journal= {arXiv preprint arXiv:1501.05065},
year = {2015}
}