Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
The University of Houston
4800, Calhoun Road, Houston, Texas, 77004, USA
The Boeing Company
Department of Mathematics
Loyola Marymount University
1 LMU Drive, Los Angeles, CA 90045, USA

Abstract. The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Ampère and Aharonov-Bohm ``quantum integrals.'' Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our differential geometric, or more accurately topological yoga can substitute successfully for statistical mechanics.

Received: January 18, 2012

AMS Subject Classification: 58-XX, 53-XX, 82-XX,

Key Words and Phrases: differential geometric, Maxwell field, Kottler-Cartan metric-independent general invariance, differentiable manifolds, Gauss-Ampère and Aharonov-Bohm ``quantum integrals''

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