Quantum Cellular Automata And Quantum Lattice Gases, Lattice QCD And Bargmann–Wigner Equations Stochastic Money Demand And The Inflation, Black Scholes From Gauge Arbitrage And Other Topics

Abstract

General covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. A more significant requirement is the principle of General Relativity that states that the laws of physics take the same form in all reference systems. This is a generalization of the principle of special relativity which states that the laws of physics take the same form in all inertial frames. In mathematics; a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. (Relation between local symmetries and constraints and the relation between Lagrangian and Hamiltonian symmetries makes it manifestly clear).

http://www.iiste.org/PDFshare/APTA-PAGENO-89172-93754.pdf