Woit · 2025-10-20 · Full contents
Collected reading chapters: 4, 5, A. Other entries open the original PDF.
- Preface · printed xiii · not collected
- 0.1 Acknowledgements · printed xvi · not collected
- 1 Introduction and Overview · printed 1 · not collected
- 1.1 Introduction · printed 1 · not collected
- 1.2 Basic principles of quantum mechanics · printed 3 · not collected
- 1.2.1 Fundamental axioms of quantum mechanics · printed 3 · not collected
- 1.2.2 Principles of measurement theory · printed 4 · not collected
- 1.3 Unitary group representations · printed 6 · not collected
- 1.3.1 Lie groups · printed 6 · not collected
- 1.3.2 Group representations · printed 7 · not collected
- 1.3.3 Unitary group representations · printed 9 · not collected
- 1.4 Representations and quantum mechanics · printed 10 · not collected
- 1.5 Groups and symmetries · printed 11 · not collected
- 1.6 For further reading · printed 11 · not collected
- 2 The Group U(1) and its Representations · printed 13 · not collected
- 2.1 Some representation theory · printed 14 · not collected
- 2.2 The group U(1) and its representations · printed 17 · not collected
- 2.3 The charge operator · printed 19 · not collected
- 2.4 Conservation of charge and U(1) symmetry · printed 21 · not collected
- 2.5 Summary · printed 23 · not collected
- 2.6 For further reading · printed 23 · not collected
- 3 Two-state Systems and SU(2) · printed 24 · not collected
- 3.1 The two-state quantum system · printed 25 · not collected
- 3.1.1 The Pauli matrices: observables of the two-state quantum system · printed 25 · not collected
- 3.1.2 Exponentials of Pauli matrices: unitary transformations of the two-state system · printed 27 · not collected
- 3.2 Commutation relations for Pauli matrices · printed 30 · not collected
- 3.3 Dynamics of a two-state system · printed 32 · not collected
- 3.4 For further reading · printed 33 · not collected
- 3.1 The two-state quantum system · printed 25 · not collected
- 4 Linear Algebra Review, Unitary and Orthogonal Groups · printed 34 · sample transcribed
- 4.1 Vector spaces and linear maps · printed 34 · sample transcribed
- 4.2 Dual vector spaces · printed 36 · sample transcribed
- 4.3 Change of basis · printed 37 · sample transcribed
- 4.4 Inner products · printed 38 · sample transcribed
- 4.5 Adjoint operators · printed 41 · sample transcribed
- 4.6 Orthogonal and unitary transformations · printed 41 · sample transcribed
- 4.6.1 Orthogonal groups · printed 42 · sample transcribed
- 4.6.2 Unitary groups · printed 43 · sample transcribed
- 4.7 Eigenvalues and eigenvectors · printed 44 · sample transcribed
- 4.8 For further reading · printed 46 · sample transcribed
- 5 Lie Algebras and Lie Algebra Representations · printed 47 · sample transcribed
- 5.1 Lie algebras · printed 48 · sample transcribed
- 5.2 Lie algebras of the orthogonal and unitary groups · printed 51 · sample transcribed
- 5.2.1 Lie algebra of the orthogonal group · printed 52 · sample transcribed
- 5.2.2 Lie algebra of the unitary group · printed 52 · sample transcribed
- 5.3 A summary · printed 53 · sample transcribed
- 5.4 Lie algebra representations · printed 54 · sample transcribed
- 5.5 Complexification · printed 59 · sample transcribed
- 5.6 For further reading · printed 61 · sample transcribed
- 6 The Rotation and Spin Groups in 3 and 4 Dimensions · printed 62 · not collected
- 6.1 The rotation group in three dimensions · printed 62 · not collected
- 6.2 Spin groups in three and four dimensions · printed 65 · not collected
- 6.2.1 Quaternions · printed 66 · not collected
- 6.2.2 Rotations and spin groups in four dimensions · printed 67 · not collected
- 6.2.3 Rotations and spin groups in three dimensions · printed 67 · not collected
- 6.2.4 The spin group and SU(2) · printed 70 · not collected
- 6.3 A summary · printed 73 · not collected
- 6.4 For further reading · printed 74 · not collected
- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field · printed 75 · not collected
- 7.1 The spinor representation · printed 75 · not collected
- 7.2 The spin 1/2 particle in a magnetic field · printed 77 · not collected
- 7.3 The Heisenberg picture · printed 80 · not collected
- 7.4 Complex projective space · printed 81 · not collected
- 7.5 The Bloch sphere · printed 85 · not collected
- 7.6 For further reading · printed 88 · not collected
- 8 Representations of SU(2) and SO(3) · printed 89 · not collected
- 8.1 Representations of SU(2): classification · printed 90 · not collected
- 8.1.1 Weight decomposition · printed 90 · not collected
- 8.1.2 Lie algebra representations: raising and lowering operators · printed 92 · not collected
- 8.2 Representations of SU(2): construction · printed 97 · not collected
- 8.3 Representations of SO(3) and spherical harmonics · printed 100 · not collected
- 8.4 The Casimir operator · printed 106 · not collected
- 8.5 For further reading · printed 108 · not collected
- 8.1 Representations of SU(2): classification · printed 90 · not collected
- 9 Tensor Products, Entanglement, and Addition of Spin · printed 109 · not collected
- 9.1 Tensor products · printed 110 · not collected
- 9.2 Composite quantum systems and tensor products · printed 112 · not collected
- 9.3 Indecomposable vectors and entanglement · printed 113 · not collected
- 9.4 Tensor products of representations · printed 114 · not collected
- 9.4.1 Tensor products of SU(2) representations · printed 114 · not collected
- 9.4.2 Characters of representations · printed 115 · not collected
- 9.4.3 Some examples · printed 116 · not collected
- 9.5 Bilinear forms and tensor products · printed 118 · not collected
- 9.6 Symmetric and antisymmetric multilinear forms · printed 119 · not collected
- 9.7 For further reading · printed 120 · not collected
- 10 Momentum and the Free Particle · printed 121 · not collected
- 10.1 The group R and its representations · printed 122 · not collected
- 10.2 Translations in time and space · printed 124 · not collected
- 10.2.1 Energy and the group R of time translations · printed 124 · not collected
- 10.2.2 Momentum and the group R3 of space translations · printed 124 · not collected
- 10.3 The energy-momentum relation and the Schrödinger equation for a free particle · printed 126 · not collected
- 10.4 For further reading · printed 128 · not collected
- 11 Fourier Analysis and the Free Particle · printed 129 · not collected
- 11.1 Periodic boundary conditions and the group U(1) · printed 130 · not collected
- 11.2 The group R and the Fourier transform · printed 133 · not collected
- 11.3 Distributions · printed 136 · not collected
- 11.4 Linear transformations and distributions · printed 138 · not collected
- 11.5 Solutions of the Schrödinger equation in momentum space · printed 140 · not collected
- 11.6 For further reading · printed 142 · not collected
- 12 Position and the Free Particle · printed 143 · not collected
- 12.1 The position operator · printed 143 · not collected
- 12.2 Momentum space representation · printed 144 · not collected
- 12.3 Dirac notation · printed 145 · not collected
- 12.4 Heisenberg uncertainty · printed 146 · not collected
- 12.5 The propagator in position space · printed 147 · not collected
- 12.6 Propagators in frequency-momentum space · printed 150 · not collected
- 12.7 Green’s functions and solutions to the Schrödinger equations · printed 153 · not collected
- 12.8 For further reading · printed 155 · not collected
- 13 The Heisenberg group and the Schrödinger Representation · printed 156 · not collected
- 13.1 The Heisenberg Lie algebra · printed 157 · not collected
- 13.2 The Heisenberg group · printed 158 · not collected
- 13.3 The Schrödinger representation · printed 159 · not collected
- 13.4 For further reading · printed 162 · not collected
- 14 The Poisson Bracket and Symplectic Geometry · printed 163 · not collected
- 14.1 Classical mechanics and the Poisson bracket · printed 163 · not collected
- 14.2 The Poisson bracket and the Heisenberg Lie algebra · printed 166 · not collected
- 14.3 Symplectic geometry · printed 168 · not collected
- 14.4 For further reading · printed 170 · not collected
- 15 Hamiltonian Vector Fields and the Moment Map · printed 171 · not collected
- 15.1 Vector fields and the exponential map · printed 172 · not collected
- 15.2 Hamiltonian vector fields and canonical transformations · printed 173 · not collected
- 15.3 Group actions on M and the moment map · printed 178 · not collected
- 15.4 Examples of Hamiltonian group actions · printed 180 · not collected
- 15.5 The dual of a Lie algebra and symplectic geometry · printed 182 · not collected
- 15.6 For further reading · printed 184 · not collected
- 16 Quadratic Polynomials and the Symplectic Group · printed 185 · not collected
- 16.1 The symplectic group · printed 186 · not collected
- 16.1.1 The symplectic group for d=1 · printed 186 · not collected
- 16.1.2 The symplectic group for arbitrary d · printed 189 · not collected
- 16.2 The symplectic group and automorphisms of the Heisenberg group · printed 191 · not collected
- 16.2.1 The adjoint representation and inner automorphisms · printed 192 · not collected
- 16.2.2 The symplectic group as automorphism group · printed 193 · not collected
- 16.3 The case of arbitrary d · printed 194 · not collected
- 16.4 For further reading · printed 196 · not collected
- 16.1 The symplectic group · printed 186 · not collected
- 17 Quantization · printed 197 · not collected
- 17.1 Canonical quantization · printed 197 · not collected
- 17.2 The Groenewold-van Hove no-go theorem · printed 200 · not collected
- 17.3 Canonical quantization in d dimensions · printed 201 · not collected
- 17.4 Quantization and symmetries · printed 201 · not collected
- 17.5 More general notions of quantization · printed 202 · not collected
- 17.6 For further reading · printed 203 · not collected
- 18 Semi-direct Products · printed 204 · not collected
- 18.1 An example: the Euclidean group · printed 204 · not collected
- 18.2 Semi-direct product groups · printed 205 · not collected
- 18.3 Semi-direct product Lie algebras · printed 207 · not collected
- 18.4 For further reading · printed 209 · not collected
- 19 The Quantum Free Particle as a Representation of the Euclidean Group · printed 210 · not collected
- 19.1 The quantum free particle and representations of E(2) · printed 211 · not collected
- 19.2 The case of E(3) · printed 216 · not collected
- 19.3 Other representations of E(3) · printed 218 · not collected
- 19.4 For further reading · printed 220 · not collected
- 20 Representations of Semi-direct Products · printed 221 · not collected
- 20.1 Intertwining operators and the metaplectic representation · printed 222 · not collected
- 20.2 Constructing intertwining operators · printed 224 · not collected
- 20.3 Explicit calculations · printed 225 · not collected
- 20.3.1 The SO(2) action by rotations of the plane for d=2 · printed 225 · not collected
- 20.3.2 An SO(2) action on the d=1 phase space · printed 227 · not collected
- 20.3.3 The Fourier transform as an intertwining operator · printed 229 · not collected
- 20.3.4 An R action on the d=1 phase space · printed 229 · not collected
- 20.4 Representations of NK, N commutative · printed 230 · not collected
- 20.5 For further reading · printed 232 · not collected
- 21 Central Potentials and the Hydrogen Atom · printed 234 · not collected
- 21.1 Quantum particle in a central potential · printed 234 · not collected
- 21.2 so(4) symmetry and the Coulomb potential · printed 238 · not collected
- 21.3 The hydrogen atom · printed 242 · not collected
- 21.4 For further reading · printed 243 · not collected
- 22 The Harmonic Oscillator · printed 244 · not collected
- 22.1 The harmonic oscillator with one degree of freedom · printed 245 · not collected
- 22.2 Creation and annihilation operators · printed 247 · not collected
- 22.3 The Bargmann-Fock representation · printed 250 · not collected
- 22.4 Quantization by annihilation and creation operators · printed 252 · not collected
- 22.5 For further reading · printed 253 · not collected
- 23 Coherent States and the Propagator for the Harmonic Oscillator · printed 254 · not collected
- 23.1 Coherent states and the Heisenberg group action · printed 254 · not collected
- 23.2 Coherent states and the Bargmann-Fock state space · printed 257 · not collected
- 23.3 The Heisenberg group action on operators · printed 259 · not collected
- 23.4 The harmonic oscillator propagator · printed 260 · not collected
- 23.4.1 The propagator in the Bargmann-Fock representation · printed 260 · not collected
- 23.4.2 The coherent state propagator · printed 261 · not collected
- 23.4.3 The position space propagator · printed 262 · not collected
- 23.5 The Bargmann transform · printed 263 · not collected
- 23.6 For further reading · printed 265 · not collected
- 24 The Metaplectic Representation and Annihilation and Creation Operators, d=1 · printed 266 · not collected
- 24.1 The metaplectic representation for d=1 in terms of a and a · printed 267 · not collected
- 24.2 Intertwining operators in terms of a and a · printed 270 · not collected
- 24.3 Implications of the choice of z,z · printed 272 · not collected
- 24.4 SU(1,1) and Bogoliubov transformations · printed 274 · not collected
- 24.5 For further reading · printed 275 · not collected
- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d · printed 276 · not collected
- 25.1 Multiple degrees of freedom · printed 277 · not collected
- 25.2 Complex coordinates on phase space and U(d)Sp(2d,R) · printed 278 · not collected
- 25.3 The metaplectic representation and U(d)Sp(2d,R) · printed 281 · not collected
- 25.4 Examples in d=2 and 3 · printed 283 · not collected
- 25.4.1 Two degrees of freedom and SU(2) · printed 283 · not collected
- 25.4.2 Three degrees of freedom and SO(3) · printed 286 · not collected
- 25.5 Normal ordering and the anomaly in finite dimensions · printed 287 · not collected
- 25.6 For further reading · printed 288 · not collected
- 26 Complex Structures and Quantization · printed 290 · not collected
- 26.1 Complex structures and phase space · printed 290 · not collected
- 26.2 Compatible complex structures and positivity · printed 293 · not collected
- 26.3 Complex structures and quantization · printed 295 · not collected
- 26.4 Complex vector spaces with Hermitian inner product as phase spaces · printed 298 · not collected
- 26.5 Complex structures for d=1 and squeezed states · printed 300 · not collected
- 26.6 Complex structures and Bargmann-Fock quantization for arbitrary d · printed 303 · not collected
- 26.7 For further reading · printed 304 · not collected
- 27 The Fermionic Oscillator · printed 305 · not collected
- 27.1 Canonical anticommutation relations and the fermionic oscillator · printed 305 · not collected
- 27.2 Multiple degrees of freedom · printed 307 · not collected
- 27.3 For further reading · printed 310 · not collected
- 28 Weyl and Clifford Algebras · printed 311 · not collected
- 28.1 The Complex Weyl and Clifford algebras · printed 311 · not collected
- 28.1.1 One degree of freedom, bosonic case · printed 311 · not collected
- 28.1.2 One degree of freedom, fermionic case · printed 312 · not collected
- 28.1.3 Multiple degrees of freedom · printed 314 · not collected
- 28.2 Real Clifford algebras · printed 315 · not collected
- 28.3 For further reading · printed 317 · not collected
- 28.1 The Complex Weyl and Clifford algebras · printed 311 · not collected
- 29 Clifford Algebras and Geometry · printed 318 · not collected
- 29.1 Non-degenerate bilinear forms · printed 318 · not collected
- 29.2 Clifford algebras and geometry · printed 320 · not collected
- 29.2.1 Rotations as iterated orthogonal reflections · printed 322 · not collected
- 29.2.2 The Lie algebra of the rotation group and quadratic elements of the Clifford algebra · printed 323 · not collected
- 29.3 For further reading · printed 325 · not collected
- 30 Anticommuting Variables and Pseudo-classical Mechanics · printed 326 · not collected
- 30.1 The Grassmann algebra of polynomials on anticommuting generators · printed 326 · not collected
- 30.2 Pseudo-classical mechanics and the fermionic Poisson bracket · printed 329 · not collected
- 30.3 Examples of pseudo-classical mechanics · printed 332 · not collected
- 30.3.1 The pseudo-classical spin degree of freedom · printed 332 · not collected
- 30.3.2 The pseudo-classical fermionic oscillator · printed 333 · not collected
- 30.4 For further reading · printed 334 · not collected
- 31 Fermionic Quantization and Spinors · printed 335 · not collected
- 31.1 Quantization of pseudo-classical systems · printed 335 · not collected
- 31.1.1 Quantization of the pseudo-classical spin · printed 339 · not collected
- 31.2 The Schrödinger representation for fermions: ghosts · printed 339 · not collected
- 31.3 Spinors and the Bargmann-Fock construction · printed 341 · not collected
- 31.4 Complex structures, U(d)SO(2d) and the spinor representation · printed 344 · not collected
- 31.5 An example: spinors for SO(4) · printed 346 · not collected
- 31.6 For further reading · printed 348 · not collected
- 31.1 Quantization of pseudo-classical systems · printed 335 · not collected
- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization · printed 349 · not collected
- 33 Supersymmetry, Some Simple Examples · printed 351 · not collected
- 33.1 The supersymmetric oscillator · printed 351 · not collected
- 33.2 Supersymmetric quantum mechanics with a superpotential · printed 354 · not collected
- 33.3 Supersymmetric quantum mechanics and differential forms · printed 356 · not collected
- 33.4 For further reading · printed 357 · not collected
- 34 The Pauli Equation and the Dirac Operator · printed 358 · not collected
- 34.1 The Pauli-Schrödinger equation and free spin 12 particles in d=3 · printed 358 · not collected
- 34.2 Solutions of the Pauli equation and representations of E(3)“0365E(3) · printed 361 · not collected
- 34.3 The E(3)“0365E(3)-invariant inner product · printed 365 · not collected
- 34.4 The Dirac operator · printed 366 · not collected
- 34.5 For further reading · printed 367 · not collected
- 35 Lagrangian Methods and the Path Integral · printed 368 · not collected
- 35.1 Lagrangian mechanics · printed 368 · not collected
- 35.2 Noether’s theorem and symmetries in the Lagrangian formalism · printed 372 · not collected
- 35.3 Quantization and path integrals · printed 374 · not collected
- 35.4 Advantages and disadvantages of the path integral · printed 377 · not collected
- 35.5 For further reading · printed 378 · not collected
- 36 Multi-particle Systems: Momentum Space Description · printed 379 · not collected
- 36.1 Multi-particle quantum systems as quanta of a harmonic oscillator · printed 380 · not collected
- 36.1.1 Bosons and the quantum harmonic oscillator · printed 380 · not collected
- 36.1.2 Fermions and the fermionic oscillator · printed 382 · not collected
- 36.2 Multi-particle quantum systems of free particles: finite cutoff formalism · printed 383 · not collected
- 36.3 Continuum formalism · printed 387 · not collected
- 36.4 Multi-particle wavefunctions · printed 391 · not collected
- 36.5 Dynamics · printed 392 · not collected
- 36.6 For further reading · printed 393 · not collected
- 36.1 Multi-particle quantum systems as quanta of a harmonic oscillator · printed 380 · not collected
- 37 Multi-particle Systems and Field Quantization · printed 394 · not collected
- 37.1 Quantum field operators · printed 395 · not collected
- 37.2 Quadratic operators and dynamics · printed 397 · not collected
- 37.3 The propagator in non-relativistic quantum field theory · printed 399 · not collected
- 37.4 Interacting quantum fields · printed 400 · not collected
- 37.5 Fermion fields · printed 402 · not collected
- 37.6 For further reading · printed 403 · not collected
- 38 Symmetries and Non-relativistic Quantum Fields · printed 404 · not collected
- 38.1 Unitary transformations on H1 · printed 405 · not collected
- 38.2 Internal symmetries · printed 406 · not collected
- 38.2.1 U(1) symmetry · printed 406 · not collected
- 38.2.2 U(n) symmetry · printed 408 · not collected
- 38.3 Spatial symmetries · printed 410 · not collected
- 38.3.1 Spatial translations · printed 411 · not collected
- 38.3.2 Spatial rotations · printed 412 · not collected
- 38.3.3 Spin 12 fields · printed 413 · not collected
- 38.4 Fermionic fields · printed 415 · not collected
- 38.5 For further reading · printed 416 · not collected
- 39 Quantization of Infinite dimensional Phase Spaces · printed 417 · not collected
- 39.1 Inequivalent irreducible representations · printed 418 · not collected
- 39.2 The restricted symplectic group · printed 420 · not collected
- 39.3 The anomaly and the Schwinger term · printed 421 · not collected
- 39.4 Spontaneous symmetry breaking · printed 422 · not collected
- 39.5 Higher order operators and renormalization · printed 423 · not collected
- 39.6 For further reading · printed 424 · not collected
- 40 Minkowski Space and the Lorentz Group · printed 425 · not collected
- 40.1 Minkowski space · printed 426 · not collected
- 40.2 The Lorentz group and its Lie algebra · printed 428 · not collected
- 40.3 The Fourier transform in Minkowski space · printed 431 · not collected
- 40.4 Spin and the Lorentz group · printed 431 · not collected
- 40.5 For further reading · printed 434 · not collected
- 41 Representations of the Lorentz Group · printed 435 · not collected
- 41.1 Representations of the Lorentz group · printed 435 · not collected
- 41.2 Dirac matrices and Cliff(3,1) · printed 440 · not collected
- 41.3 For further reading · printed 443 · not collected
- 42 The Poincaré Group and its Representations · printed 444 · not collected
- 42.1 The Poincaré group and its Lie algebra · printed 445 · not collected
- 42.2 Irreducible representations of the Poincaré group · printed 447 · not collected
- 42.3 Classification of representations by orbits · printed 450 · not collected
- 42.3.1 Positive energy time-like orbits · printed 451 · not collected
- 42.3.2 Negative energy time-like orbits · printed 452 · not collected
- 42.3.3 Space-like orbits · printed 452 · not collected
- 42.3.4 The zero orbit · printed 453 · not collected
- 42.3.5 Positive energy null orbits · printed 453 · not collected
- 42.3.6 Negative energy null orbits · printed 454 · not collected
- 42.4 For further reading · printed 455 · not collected
- 43 The Klein-Gordon Equation and Scalar Quantum Fields · printed 456 · not collected
- 43.1 The Klein-Gordon equation and its solutions · printed 456 · not collected
- 43.2 The symplectic and complex structures on M · printed 461 · not collected
- 43.3 Hamiltonian and dynamics of the Klein-Gordon theory · printed 465 · not collected
- 43.4 Quantization of the Klein-Gordon theory · printed 466 · not collected
- 43.5 The scalar field propagator · printed 469 · not collected
- 43.6 Interacting scalar field theories: some comments · printed 471 · not collected
- 43.7 For further reading · printed 472 · not collected
- 44 Symmetries and Relativistic Scalar Quantum Fields · printed 473 · not collected
- 44.1 Internal symmetries · printed 474 · not collected
- 44.1.1 SO(m) symmetry and real scalar fields · printed 474 · not collected
- 44.1.2 U(1) symmetry and complex scalar fields · printed 476 · not collected
- 44.2 Poincaré symmetry and scalar fields · printed 479 · not collected
- 44.2.1 Translations · printed 481 · not collected
- 44.2.2 Rotations · printed 482 · not collected
- 44.2.3 Boosts · printed 482 · not collected
- 44.3 For further reading · printed 483 · not collected
- 44.1 Internal symmetries · printed 474 · not collected
- 45 U(1) Gauge Symmetry and Electromagnetic Fields · printed 484 · not collected
- 45.1 U(1) gauge symmetry · printed 484 · not collected
- 45.2 Curvature, electric and magnetic fields · printed 486 · not collected
- 45.3 Field equations with background electromagnetic fields · printed 487 · not collected
- 45.4 The geometric significance of the connection · printed 489 · not collected
- 45.5 The non-Abelian case · printed 491 · not collected
- 45.6 For further reading · printed 493 · not collected
- 46 Quantization of the Electromagnetic Field: the Photon · printed 494 · not collected
- 46.1 Maxwell’s equations · printed 494 · not collected
- 46.2 The Hamiltonian formalism for electromagnetic fields · printed 496 · not collected
- 46.3 Gauss’s law and time-independent gauge transformations · printed 498 · not collected
- 46.4 Quantization in Coulomb gauge · printed 500 · not collected
- 46.5 Space-time symmetries · printed 503 · not collected
- 46.5.1 Time translations · printed 503 · not collected
- 46.5.2 Spatial translations · printed 504 · not collected
- 46.5.3 Rotations · printed 505 · not collected
- 46.6 Covariant gauge quantization · printed 505 · not collected
- 46.7 For further reading · printed 509 · not collected
- 47 The Dirac Equation and Spin 12 Fields · printed 511 · not collected
- 47.1 The Dirac equation in Minkowski space · printed 511 · not collected
- 47.2 Majorana spinors and the Majorana field · printed 514 · not collected
- 47.2.1 Majorana spinor fields in momentum space · printed 517 · not collected
- 47.2.2 Quantization of the Majorana field · printed 519 · not collected
- 47.3 Weyl spinors · printed 520 · not collected
- 47.4 Dirac spinors · printed 523 · not collected
- 47.5 For further reading · printed 524 · not collected
- 48 An Introduction to the Standard Model · printed 525 · not collected
- 48.1 Non-Abelian gauge fields · printed 525 · not collected
- 48.2 Fundamental fermions · printed 526 · not collected
- 48.3 Spontaneous symmetry breaking · printed 526 · not collected
- 48.4 Unanswered questions and speculative extensions · printed 527 · not collected
- 48.4.1 Why these gauge groups and couplings? · printed 527 · not collected
- 48.4.2 Why these representations? · printed 528 · not collected
- 48.4.3 Why three generations? · printed 528 · not collected
- 48.4.4 Why the Higgs field? · printed 528 · not collected
- 48.4.5 Why the Yukawas? · printed 529 · not collected
- 48.4.6 What is the dynamics of the gravitational field? · printed 529 · not collected
- 48.5 For further reading · printed 529 · not collected
- 49 Further Topics · printed 530 · not collected
- 49.1 Connecting quantum theories to experimental results · printed 530 · not collected
- 49.2 Other important mathematical physics topics · printed 531 · not collected
- A Conventions · printed 533 · sample transcribed
- A.1 Bilinear forms · printed 533 · sample transcribed
- A.2 Fourier transforms · printed 534 · sample transcribed
- A.3 Symplectic geometry and quantization · printed 534 · sample transcribed
- A.4 Complex structures and Bargmann-Fock quantization · printed 535 · sample transcribed
- A.5 Special relativity · printed 536 · sample transcribed
- A.6 Clifford algebras and spinors · printed 536 · sample transcribed
- B Exercises · printed 537 · not collected
- B.1 Chapters 1 and 2 · printed 537 · not collected
- B.2 Chapters 3 and 4 · printed 538 · not collected
- B.3 Chapters 5 to 7 · printed 539 · not collected
- B.4 Chapter 8 · printed 540 · not collected
- B.5 Chapter 9 · printed 541 · not collected
- B.6 Chapters 10 to 12 · printed 542 · not collected
- B.7 Chapters 14 to 16 · printed 543 · not collected
- B.8 Chapter 17 · printed 545 · not collected
- B.9 Chapters 18 and 19 · printed 546 · not collected
- B.10 Chapters 21 and 22 · printed 546 · not collected
- B.11 Chapter 23 · printed 548 · not collected
- B.12 Chapters 24 to 26 · printed 548 · not collected
- B.13 Chapters 27 and 28 · printed 549 · not collected
- B.14 Chapters 29 to 31 · printed 550 · not collected
- B.15 Chapters 33 and 34 · printed 551 · not collected
- B.16 Chapter 36 · printed 552 · not collected
- B.17 Chapters 37 and 38 · printed 552 · not collected
- B.18 Chapters 40 to 42 · printed 553 · not collected
- B.19 Chapters 43 and 44 · printed 554 · not collected
- B.20 Chapters 45 and 46 · printed 555 · not collected
- B.21 Chapter 47 · printed 555 · not collected