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In this book the author derives, under the classical non-relativistic consideration of the space-time, general forms of the most common physical laws invariant under the changes of inertial or non-inertial coordinate systems, both in the classical and the quantum regime. Important examples of such invariant physical laws are the Maxwell Equations, Newtonian gravity as well as several more complicated models of gravity and many other physical laws including many of the laws of quantum mechanics, thermodynamics and statistical physics, continuum mechanics, and optics. Moreover, several basic laws of relativistic physics, both in the classical and quantum regimes can be still formulated invariantly under the non-relativistic consideration of space-time. These include the classical relativistic Second Law of Newton and the quantum Dirac and Klein--Gordon equations for relativistic particles, including their interaction with the external gravitational field. In particular, we introduce the Hamiltonian formulation of the Dirac equation, and moreover, were able to formulate the Dirac equation for multiple particles, similarly to what was done for the Schroedinger equation of the non-relativistic quantum mechanics. One of the goals of this work is to provide a self-contained and simple mathematical formulation of the most general physical laws in a manner understandable to the reader familiar only with basic calculus, classical mechanics and basic elements of non-relativistic quantum mechanics. 

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9783031614064

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Arkady Poliakovsky is an Associate Professor at the Department of Mathematics at Ben-Gurion University of the Negev, Be'er Sheva, Israel. His main specialization is Calculus of Variations and Partial Differential Equations. However he is also interested in Physics, Mathematical Physics, Fluid Mechanics, Differential Geometry and Tensor Calculus. Prof. Poiliakovsky was born in Russia in 1978. He immigrated with his parents to Israel in 1993 and obtained all his academic degrees from the Department of Mathematics of the Technion - I.I.T., Haifa, Israel: his primary Bachelor degree (summa cum laude) in 1999, a M.Sc. degree in 2002, and a Ph.D. in 2005. During the period 2005-2012 he held Post-Doc positions at various universities: Paris VI, University of Zurich, University of Duisburg-Essen, University of Bonn, and University of Rome - Tor Vergata. He was appointed to a Tenure Track position at Ben Gurion University of the Negev (Be'er Sheva, Israel) in 2012 (Senior Lecturer till 2016, Associate Professor since 2016, tenured since 2017). He obtained secondary Bachelor degrees in Physics and Computer Science in Technion, Haifa at 2017.

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