(Ebook PDF) Mathematical Physics with Differential Equations 1st edition by Yisong Yang 019287263X 9780192872630 full chapters

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ISBN-10 :  019287263X 

ISBN-13 : 9780192872630

Author:  Yisong Yang 

Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike.

Mathematical Physics with Differential Equations 1st Table of contents:

1 Hamiltonian systems and applications
1.1 Motion of massive particle
1.2 Many-body problem
1.3 Kepler’s laws of planetary motion
1.4 Helmholtz–Kirchhoff vortex model
1.5 Partition function and thermodynamics
1.6 Dynamic modeling of DNA denaturation
2 Schrödinger equationand quantum mechanics
2.1 Path to quantum mechanics
2.2 Schrödinger equation
2.3 Quantum many-body problem
2.4 Hartree–Fock method
2.5 Thomas–Fermi approach
2.6 Density functional theory
3 Maxwell equations, Dirac monopole, and gauge fields
3.1 Maxwell equations and electromagnetic duality
3.2 Dirac monopole and strings
3.3 Charged particle in electromagnetic field
3.4 Removal of Dirac strings and charge quantization
3.5 Schwinger dyons and extended charge quantization formula
3.6 Aharonov–Bohm effect
4 Special relativity
4.1 Inertial frames, Minkowski spacetime,and Lorentz boosts
4.2 Line element, proper time, and consequences
4.3 Relativistic mechanics
4.4 Doppler effects
5 Abelian gauge field equations
5.1 Spacetime, covariance, and invariance
5.2 Relativistic field equations
5.3 Coupled nonlinear hyperbolic and elliptic equations
5.4 Symmetry breaking
5.5 Higgs mechanism
6 Dirac equations
6.1 Pauli matrices, spinor fields, and Diracequation
6.2 Action, probability, and current densities
6.3 Special solutions
6.4 Dirac equation coupled with gaugefield
6.5 Dirac equation in Weyl representation
6.6 Nonlinear Dirac equations
7 Ginzburg–Landau equations for superconductivity
7.1 Perfect conductors, superconductors, and London equations
7.2 Superconductors and Ginzburg–Landau equations
7.3 Classification of superconductivityby surface energy
7.4 Mixed state and its magnetic characterizations
7.5 Some generalized Ginzburg–Landau equations
8 Magnetic vortices in Abelian Higgs theory
8.1 Energy partition, flux quantization,and topological properties
8.2 Vortex-lines, solitons, and particles
8.3 Radially symmetric solutions
8.4 From monopole confinement to quarkconfinement
9 Non-Abelian gauge field equations
9.1 Yang–Mills theory
9.2 Georgi–Glashow model
9.3 ‘t Hooft–Polyakov monopole and Julia–Zeedyon
9.4 Monopoles and dyons in BPS limit
9.5 Weinberg–Salam electroweak equations
10 Einstein equations and related topics
10.1 Einstein field equations
10.2 Cosmological consequences
10.3 Schwarzschild black-hole solution
10.4 Reissner–Nordström solution
10.5 Kerr solution
10.6 Gravitational mass and Penrose bounds
10.7 Gravitational waves
10.8 Scalar-wave matters as quintessence
11 Charged vortices and Chern–Simons equations
11.1 Julia–Zee theorem
11.2 Chern–Simons term
11.3 Dually charged vortices
11.4 Rubakov–Tavkhelidze problem
12 Skyrme model and related topics
12.1 Derrick theorem and Pohozaev identity
12.2 Skyrme model
12.3 Knots in Faddeev model
12.4 Other fractional-exponent growth lawsand knot energies
12.5 Q-balls
13 Strings and branes
13.1 Motivation and relativistic motion of freeparticle as initial setup
13.2 Nambu–Goto strings
13.3 p-branes
13.4 Polyakov strings and branes
13.5 Equations of motion with interactions
14 Born–Infeld theory of electromagnetism
14.1 Resolution of energy divergence problemof point charges
14.2 Some illustrative calculations
14.3 Dyonic point charge
14.4 Formalism based on invariance
14.5 Generalized Bernstein problem
14.6 Born–Infeld term and virial identities
14.7 Integer-squared law for global Born–Infeld vortices
14.8 Electrically charged black hole solutions
14.9 Dyonic black hole solutions
14.10 Generalized Born–Infeld theoriesand applications
14.11 Electromagnetic asymmetry by virtueof point charges
14.12 Charged black holes
14.13 Relegation of curvature singularities of charged black holes
14.14 Cosmology driven by scalar-wave matters as k-essence
14.15 Finite-energy dyonic point charge
14.16 Dyonically charged black holes with relegated singularities
15 Canonical quantization of fields
15.1 Quantum harmonic oscillator
15.2 Canonical quantization
15.3 Field equation formalism
15.4 Quantization of Klein–Gordon equation
15.5 Quantization of Schrödinger equation
15.6 Quantization of electromagnetic fields
15.7 Thermodynamics of harmonic oscillator

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