The Six Core Theories of Modern Physics Book

	Preface
	Notational Conventions
1	Mathematics	1
	Vector Analysis	1
	Linear Operators on Inner-Product Spaces	7
	Green's Functions	22
	The Calculus of Variations	27
	Random Walk	30
	Functional Calculus	32
	Gaussian Random Processes	44
	Cartesian Tensors	53
2	Classical Mechanics	59
	Euler-Lagrange Equation: First Version	59
	Hamilton's Principle	61
	Multiple Particles in Three Dimensions	62
	Euler-Lagrange Equation: Second Version	63
	Hamilton's Equations	65
	Poisson Brackets	68
3	Electricity and Magnetism	71
	The Electrostatic Field	73
	The Magnetostatic Field	76
	The Electromagnetic Field	77
	The Macroscopic Maxwell's Equations	80
	Gauge Transformations	90
4	Quantum Mechanics	103
	Fundamental Assumptions	103
	Schrodinger's Equation	109
	Next Steps	113
	Momentum Representation	113
	Operators	115
	The Uncertainty Principle	125
	The Schrodinger and Heisenberg Pictures	128
	Time-Varying Forcing	131
5	Statistical Physics	137
	Historical Context	137
	Thermodynamics	139
	Equilibrium Statistical Mechanics	151
	Nonequilibrium Statistical Mechanics	158
	Quantum Statistical Mechanics	164
6	Special Relativity	173
	Einstein's Postulates and First Consequences	173
	Theories Must Be Covariant	185
7	Quantum Field Theory	201
	The Lagrangian for a Mechanical Field	203
	The Field-Transition Amplitude	205
	The Feynman Propagator	208
	Second Quantization	213
	Interacting Fields	216
	Antiparticles	219
	Additional Reading	223
	Symbol Index	227
	Equation Index	229
	Subject Index	231