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Quantum Mechanics (Coming soon)
Chapter 1 Old Qunatum Theory: Bohr's correspondence principle, etc.
Chapter 2 Basic Concepts of Quantum Mechanics: Born’s probabilistic interpretation, Robertson’s inequality, density matrix, Wigner function, uncertainty relation, etc.
Chapter 3 The Schrödinger Equation: Tunneling effect, probability current density, Ritz’s variational principle, symmetry and conservation laws, etc.
Chapter 4 One-Dimensional Quantum Systems: Well-type potential, Morse potential, soliton-type potential, step potential, Woods-Saxon-type potential, one-dimensional harmonic oscillator, coherent states, squeezed states, phase operators, etc.
Chapter 5 Angular Momentum: Fundamentals of group theory, spherical harmonics, spin, addition of angular momenta, Clebsch-Gordan coefficients, Wigner D-function, Racah’s formula, Wigner-Eckart theorem, etc.
Chapter 6 Motion in a Central Force Field: Spherical wave solutions, Coulomb field (hydrogen atom), dynamical symmetries, three-dimensional harmonic oscillator, etc.
Chapter 7 Perturbation Theory: The von Neumann-Wigner theorem, Stark effect (Kotani’s and Sunagawa’s methods), van der Waals force, nuclear deformation, secular equations, linear Stark effect, Zeeman effect, hydrogen molecular ion, LCAO approximation, calculations of overlap, Coulomb, and resonance integrals, (anti)bonding orbitals, Brillouin-Wigner perturbation theory, interaction picture, Fermi’s golden rule, the “uncertainty relation" between time and energy, the adiabatic theorem and adiabatic approximation, etc.
Chapter 8 WKB Approximation: The Bohr-Sommerfeld quantization condition, tunneling effect, Gamow transmission coefficient, α decay, bounce, instanton, anharmonic oscillator, Hawking radiation, etc.
Chapter 9 Path Integrals: The semiclassical approximation in the path integral formalism, Feynman kernel, Feynman diagrams, perturbative expansion for the anharmonic oscillator, central force fields and path integrals, etc.
Chapter 10 Identical Particles: The principle of indistinguishability, Slater determinant, exchange interactions, Young diagrams, etc.
Chapter 11 (In preparation) Atoms and Molecules: Variational methods, etc.
Chapter 12 Charged Particles in an Electromagnetic Field: g-factor, charged particles in a magnetic field, Landau levels, Larmor precession, Berry phase, magnetic monopoles, Aharonov-Bohm effect, etc.
Chapter 13 (In preparation) Scattering Theory: Born approximation, Coulomb scattering, scattering of identical particles, etc.
Chapter 14 Quantum Theory of Radiation: Quantization of the electromagnetic field, multipole expansion, Einstein coefficients, Kramers-Heisenberg formula, Thomson scattering, Rayleigh scattering, resonant scattering, Lamb shift, etc.
Chapter 15 The Dirac Equation: Tani-Foldy-Wouthuysen transformation, magic numbers, Dirac particles in a Coulomb field (hydrogen atom), fine structure, hyperfine structure, etc.
Quantum Field Theory (In preparation – intended for readers with a background in QM)
Chapter 1: Introduction
Part I: Scalar Fields
Chapter 2: Canonical Quantization: Klein-Gordon Equation, Analytical Mechanics of Fields, Free Real Scalar Field, Free Propagator, φ⁴ Theory, etc.
Chapter 3: Path Integral Quantization: Path Integrals in QFT, Generating Functional for Green’s Functions, Feynman Diagrams, Feynman Rules, Connected Green’s Functions, 1PI Diagrams and Effective Action, Effective Potential, Finite-Temperature Effective Potential, etc.
Chapter 4: Renormalization: Additional Feynman Rules, Cut-Off Regularization, Pauli-Villars Regularization, Dimensional Regularization, Integral Formulas for Dimensional Regularization and Their Proofs, Examples of Dimensional Regularization Calculations, etc.
Part II: Spinor Fields
Chapter 5: Classical Theory of Spinor Fields: Weyl Spinors, Dirac Spinors, Majorana Spinors, Gamma Matrices and Clifford Algebra, etc
Chapter 6: Quantum Theory of Spinor Fields: Dirac Equation, Plane Wave Solutions of the Dirac Equation, Properties and Proofs of u and v, Feynman Rules for Spinor Fields, Chirality, etc.
Part III: Quantum Electrodynamics
Chapter 7: U(1) Gauge Theory: Covariant Derivative, Gauge Fields, Hilbert Space with Indefinite Metric, Propagator for the U(1) Gauge Field, etc.
Chapter 8: Feynman Diagrams in QED: Feynman Rules for QED, Examples of Tree-Level Diagrams (electron-muon scattering, Compton scattering), Examples of One-Loop Diagrams (self-energy, vacuum polarization, vertex correction), bremsstrahlung, Ward-Takahashi identity, running coupling constant, Landau pole, etc.
Part IV: Non-Abelian Gauge Fields
Chapter 9: Classical Theory of Non-Abelian Gauge Fields: Fundamental and Adjoint Representations, SU(N) Gauge Theory, Field Strength (Curvature), Yang-Mills Theory, Canonical Formalism for Constrained Singular Systems, First-Class and Second-Class Constraints, etc.
Chapter 10: Quantum Theory of Non-Abelian Gauge Fields: Faddeev-Popov ghosts, BRST symmetry and BRST quantization, Nakanishi-Lautrup field, Kugo and Ojima's Auxiliary Condition, One-Loop β-Function Calculation in SU(N) Gauge Theory (for finite-mass matter field and general gauge parameter), asymptotic freedom, etc.
Part V: Particle Theory
Chapter 11 (In preparation) The Standard Model: Spontaneous Symmetry Breaking, the Higgs Mechanism, the Weinberg-Salam Model, Quantum Chromodynamics (QCD), gluon fusion, anomalies, etc.
Thermal Field Theory (In preparation – intended for readers with a background in QM and QFT)
Chapter 1: Introduction
Chapter 2: Imaginary-Time Formalism in Quantum Field Theory: Finite-Temperature One-Loop Effective Potential, etc.
Chapter 3: Finite-Temperature Scalar Field: Self-Energy of the Scalar Field, Effective Propagator for the Scalar Field, Ring (Daisy) Resummation, Dyson-Schwinger Equation, etc.
Chapter 4: Finite-Temperature Dirac and Gauge Fields: Effective Propagator for Dirac Fields, Separation of Transverse and Longitudinal Components, Effective Propagator for Gauge Fields, Construction of Frequency Sum Formulas, etc.
Chapter 5: Collective Excitations in a Thermal Bath: Self-Energies of photon, electron, and gluon, structure functions, etc.
Chapter 6: Hard Thermal Loops---Approximation and Resummation: Three-Point and Four-Point Functions in QED, Three-Point and Four-Point Functions in QCD, Ward-Takahashi identities, effective vertices, effective perturbation theory, gluon damping rate, etc.
Chapter 7: Cosmological Applications: white dwarfs, quark-gluon plasma, electroweak phase transition, electroweak baryogenesis, etc.
(Additional content forthcoming)
Baryon Asymmetry of the Universe (In preparation – intended for readers with a background in QM, QFT and TFT)
Chapter 1 Introduction
Part I Representative Scenarios
Chapter 2 Leptogenesis: decays, inverse decays, Delta L=1 scatterings, Delta L=2 scatterings, solar and atmospheric neutrinos, neutrinoless double beta decay, one-loop calculation of CP asymmetry, Davidson--Ibarra bound and its extensions, neutrino mass window, flavor effects, etc.
Chapter 3 Electroweak Baryogenesis: finite-temperature one-loop effective potential, condition for the electroweak phase transition to be first order, ring (daisy) resummation of the effective potential, baryon number preservation criterion (BNPC), two-loop QCD corrections to the EWPT, supersymmetric two-Higgs-doublet models, Barr--Zee graphs and two-loop EDM, gluon fusion and loop interference calculations, etc.
Part II Other Scenarios
Chapter 4 Electromagnetic Leptogenesis: UV completions, effective field theory (EFT), gauge-invariant effective operators and one-loop matching of Wilson coefficients, one-loop multiplicative renormalization in EFT, renormalization group equations (RGEs) of Wilson coefficients, electroweak symmetry breaking (EWSB), dipole couplings, computation of total decay width of right-handed neutrinos and flavor-dependent CP asymmetries ε in the broken phase, identical structural suppression in Γ and ε due to dipole couplings, flavor effects (decoherence, spectator effects), sphaleron processes (conversion coefficient 12/37 in the broken phase), competition between CP sources and washout leading to plateau formation, suppression of the baryon asymmetry, … (to be completed)
Chapter 5 (In preparation)
Chapter 6 (In preparation)