Arkady Poliakovsky

The Laws of Gravity and Electromagnetism (eBook, PDF)

A Non-relativistic Model Invariant Under the Change of Inertial and Non-inertial Coordinate Systems

• Format: PDF

Produktbeschreibung

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. Some important examples of such invariant Physical Laws are the Maxwell Equations, the Newtonian gravity as well as several more complicated models of gravity and many other Physical Laws including many Laws of Quantum Mechanics, Thermodynamics and Statistical Physics, Continuum Mechanics, Optics et. al. Moreover, several basic Laws of Relativistic Physics, both in the classical and Quantum levels can be still formulated invariant under the non-relativistic consideration of the space-time, like the Classical Relativistic Second Law of Newton and Quantum Dirac and Klein--Gordon equations for relativistic particles, including their interaction with the outer gravitational field. In particular, we introduce the Hamiltonian formulation of the Dirac equation, and moreover, we 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 the general 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 some basic elements of non-relativistic Quantum Mechanics.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 641
• Erscheinungstermin: 26. Oktober 2024
• Englisch
• ISBN-13: 9783031614071
• Artikelnr.: 71996707

Autorenporträt

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.

Inhaltsangabe

Introduction.- Notations and preliminaries.- Transformations of scalar and vector elds under the change of inertial or noninertial cartesian coordinate system.- Gravity revised.- Maxwell equations revised.- Maxwell equations in non-inertial cartesian coordinate systems.- Scalar and vectorial electromagnetic potentials.- Lagrangian of the Electromagnetic eld.- Local gravitational time and Maxwell equations in a non-rotating coordinate system.- Motion of particles in external gravitational-electromagnetic eld.- Relation between the gravitational and inertial masses and conservation laws.- Lagrangian of the unied Gravitational-Electromagnetic eld.- Covariant formulation of the physical laws in the four-dimensional non-relativistic space-time.- Relativistic-like Dirac equation.- Thermodynamics of a moving continuum medium.- Maxwell equations in the presence of Dielectrics and/or Magnetics.- Some further consequences of Maxwell equations.- Appendix.