Document Type
Article
Publication Date
2012
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-Amp`ere 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.
Original Publication Citation
Sholar, S., H. Rahimizadeh, E. J. Post,“On Levi-Civita’s Alternating Symbol, Schouten’s Alternating Unit Tensors, CPT, and Quantization.” International Journal of Pure and Applied Mathematics, 78(6), 2012, 895-907.
Publisher Statement
© 2012 Academic Publications, Ltd.
Digital Commons @ LMU & LLS Citation
Post, Evert Jan; Sholar, Stan; Rahimizadeh, Hooman; and Berg, Michael, "On Levi-Civita’s Alternating Symbol, Schouten’s Alternating Unit Tensors, CPT, and Quantization" (2012). Mathematics, Statistics and Data Science Faculty Works. 70.
https://digitalcommons.lmu.edu/math_fac/70
