The Six Core Theories of Modern Physics

Texte du rabat

The Six Core Theories of Modern Physics reviews all the key areas of physics in one place. It provides a brief, clear, and self-contained summary of the basic theoretical structures of classical mechanics, electricity and magnetism, quantum mechanics, statistical physics, special relativity, and quantum field theory. In addition, the mathematics required for these areas is conveniently summarized in the initial chapter. Advanced undergraduates or beginning graduate students can use The Six Core Theories of Modern Physics as a supplement to the standard texts or for an unclutterred, succinct review of the key areas. Professionals in such quantitative sciences as chemistry, engineering, computer science, applied mathematics, and biophysics who need to brush up on the essentials of a particular area will find most of the required background material, including the mathematics. Chapters may be read in any order, although the order in which they appear indicates roughly their level of difficulty and the extent to which a particular chapter depends on knowledge and sophistication gained in preceding ones. Each chapter consists of a main part, which gives the core theory, and optional sections which are more advanced and specialized.

Résumé
This text presents a summary of the basic theoretical structures of classical mechanics, electricity and magnetism, quantum mechanics, statistical physics, special relativity and modern field theories.

Contenu
Preface; Notational Conventions. Part 1 Mathematics: Vector Analysis; Linear Operators on Inner-Product Spaces; Green's Functions; The Calculus of Variations; Random Walk; Functional Calculus; Gaussian Random Processes; Cartesian Tensors. Part 2 Classical Mechanics: Euler-Lagrange Equation: First Version; Hamilton's Principle; Multiple Particles in Three Dimensions; Euler-Lagrange Equation: Second Version; Hamilton's Equations; Poisson Brackets. Part 3 Electricity and Magnetism: The Electrostatic Field; The Magnetostatic Field; The Electromagnetic Field; The Macroscopic Maxwell's Equations; Gauge Transformations. Part 4 Quantum Mechanics: Fundamental Assumptions; Schrodinger's Equation; Next Steps; Momentum Representation; Operators; The Uncertainty Principle; The Schrodinger and Heisenberg Pictures; Time-Varying Forcing. Part 5 Statistical Physics; Historical Context; Thermodynamics; Equilibrium Statistical Mechanics; Nonequilibrium Statistical Mechanics; Quantum Statistical Mechanics. Part 6 Special Relativity: Einstein's Postulates and First Consequences; Theories Must Be Covariant. Part 7 Quantum Field Theory: The Lagrangian for a Mechanical Field; The Field-Transition Amplitude; The Feynman Propagator; Second Quantisation; Interacting Fields; Antiparticles. Additional Reading; Symbol Index; Equation Index; Subject Index.