Harish Parthasarathy | Category: MathematicsBook Details

ISBN: 9789386677556

YOP: 2018

Pages: 659

Order also on

About the book: This is a textbook and a reference book for researchers working in the eld of general relativity, quantum mechanics and quantum gravity. A major part of the book deals with the formulation of special relativistic mechanics, special relativistic uid dynamics and its generalization to general relativity where the gravitational eld is described by a metric tensor. Emphasis is laid on the fact that the general theory of relativity is of tensorial character under all dieomorphisms of space-time and hence its eld equations, namely the Einstein eld equations for gravitation, the Maxwell equations in a curved space-time geometry and the uid dynamical equations in curved space time are all valid for all observers in the universe. Perturbation theoretic techniques for solving the hydrodynamical equations in curved space-time are discussed. Plasma physics in general relativity is discussed and further, the interaction of the gravitational eld with a photon bath modeled using the Hudson-Parthasarathy quantum stochastic calculus is also discussed. Waveguides in a gravitational eld are also considered. The emphasis throughout is on the fact that matter generates a gravitational field described by a metric that has a non-vanishing curvature tensor and hence such space-times are inherently curved, ie, cannot be transformed into Minkowsian form. There is a section on quantum mechanics and quantum eld theory which introduces

supersymmetry and quantum gravity to the reader. The reader after going through this book will be sufficiently well equipped to start research in quantum gravity, ie, background independent physics which is as yet an unsolved problem owing to renormalization problems.

Part I: The special and general theories of relativity with applications

The special theory of relativity

The General theory of relativity.

Engineering Applications

Part II: Some basic problems in electromagnetics related to general relativity

Part III: Basic problems in algebra, geometry and differential equations

Part IV: Quantum mechanics

Appendices

About the book: This is a textbook and a reference book for researchers working in the eld of general relativity, quantum mechanics and quantum gravity. A major part of the book deals with the formulation of special relativistic mechanics, special relativistic uid dynamics and its generalization to general relativity where the gravitational eld is described by a metric tensor. Emphasis is laid on the fact that the general theory of relativity is of tensorial character under all dieomorphisms of space-time and hence its eld equations, namely the Einstein eld equations for gravitation, the Maxwell equations in a curved space-time geometry and the uid dynamical equations in curved space time are all valid for all observers in the universe. Perturbation theoretic techniques for solving the hydrodynamical equations in curved space-time are discussed. Plasma physics in general relativity is discussed and further, the interaction of the gravitational eld with a photon bath modeled using the Hudson-Parthasarathy quantum stochastic calculus is also discussed. Waveguides in a gravitational eld are also considered. The emphasis throughout is on the fact that matter generates a gravitational field described by a metric that has a non-vanishing curvature tensor and hence such space-times are inherently curved, ie, cannot be transformed into Minkowsian form. There is a section on quantum mechanics and quantum eld theory which introduces

supersymmetry and quantum gravity to the reader. The reader after going through this book will be sufficiently well equipped to start research in quantum gravity, ie, background independent physics which is as yet an unsolved problem owing to renormalization problems.

Part I: The special and general theories of relativity with applications

The special theory of relativity

The General theory of relativity.

Engineering Applications

Part II: Some basic problems in electromagnetics related to general relativity

Part III: Basic problems in algebra, geometry and differential equations

Part IV: Quantum mechanics

Appendices