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The Map of Particle Physics | The Standard Model Explained - YouTube
Quantum electrodynamics
[[Quantum chromodynamics]]

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Quantum Field Theory
Quantum fields
Particles as excitations of fields
Creation and annihilation operators
Fock space
Canonical quantization
Path integral formulation
Lagrangian Formalism
Lagrangian density
Action principle
Euler-Lagrange equations
Noether's theorem
Symmetries and conservation laws
Gauge Theory
Gauge invariance
Gauge fields (vector potentials)
Gauge transformations
Covariant derivatives
Field strength tensors
Yang-Mills theory
Lie Groups and Algebras
SU(3) × SU(2) × U(1) gauge group
Lie group generators
Lie algebra commutation relations
Structure constants
Representations of Lie groups
Fermion Fields
Dirac equation
Spinors (Dirac, Weyl, Majorana)
Gamma matrices
Chirality and handedness
Left-handed and right-handed fermions
Lepton fields (electron, muon, tau, neutrinos)
Quark fields (up, down, charm, strange, top, bottom)
Higgs Mechanism
Higgs field
Higgs potential
Spontaneous symmetry breaking
Goldstone bosons
Higgs boson
Yukawa couplings
Electroweak Theory
SU(2)L × U(1)Y gauge group
Weak isospin and hypercharge
Weinberg angle (weak mixing angle)
W and Z bosons
Electroweak symmetry breaking
Charged and neutral currents
Quantum Chromodynamics (QCD)
SU(3) color gauge group
Gluon fields
Color charge
Quark-gluon interactions
Asymptotic freedom
Confinement
Renormalization
Regularization (dimensional, cutoff, etc.)
Renormalization group equations
Running coupling constants
Beta functions
Anomalous dimensions
Feynman Diagrams
Propagators
Vertices
External and internal lines
Loop diagrams
Feynman rules
Symmetries and Conservation Laws
Charge conjugation (C)
Parity (P)
Time reversal (T)
CPT theorem
Baryon and lepton number conservation
Flavor symmetries
Vacuum and Perturbation Theory
Vacuum state
Vacuum expectation values
Perturbative expansion
Dyson series
Wick's theorem
Normal ordering
Functional Methods
Generating functionals
Green's functions
Connected Green's functions
Effective action
Legendre transformation
1PI and 2PI effective actions
Anomalies
Chiral anomaly
Axial anomaly
Gauge anomaly
Anomaly cancellation
Regularization and Renormalization Schemes
Dimensional regularization
Pauli-Villars regularization
Lattice regularization
MS and MS-bar schemes
Renormalization conditions
Effective Field Theories
Operator product expansion
Wilson coefficients
Renormalization group running
Matching conditions
Fermi theory of weak interactions
Chiral perturbation theory
Unitarity and S-matrix
S-matrix
Unitarity
Optical theorem
Cutkosky rules
Dispersion relations
Symmetry Breaking
Explicit symmetry breaking
Spontaneous symmetry breaking
Nambu-Goldstone bosons
Chiral symmetry breaking
Electroweak symmetry breaking
Gauge Fixing and Ghost Fields
Faddeev-Popov procedure
Gauge-fixing terms
Faddeev-Popov determinant
Ghost fields
BRST symmetry
Quantum Anomalies and Topology
Chiral anomaly
Axial anomaly
Gauge anomaly
Anomaly cancellation
Instantons
Topological charges
Quantum Field Theory
Quantum fields as operator-valued distributions
Equal-time commutation relations (ETCRs)
Canonical quantization procedure
Path integral quantization
Feynman's sum over histories approach
Schwinger-Dyson equations
Källén-Lehmann spectral representation
Haag's theorem and the interaction picture
Wick rotation and Euclidean quantum field theory
Lagrangian Formalism
Principle of least action
Euler-Lagrange equations of motion
Noether's first theorem (global symmetries)
Noether's second theorem (local symmetries)
Energy-momentum tensor
Belinfante-Rosenfeld tensor
Canonical stress-energy tensor
Hilbert stress-energy tensor
Gauge Theory
Principal fiber bundles
Connection 1-forms and gauge potentials
Parallel transport and Wilson lines
Holonomies and Wilson loops
Curvature 2-forms and field strength tensors
Chern-Simons forms and topological terms
't Hooft symbols and instantons
BPST instanton solution
't Hooft-Polyakov monopole solution
Lie Groups and Algebras
Cartan classification of Lie algebras
Killing form and Cartan-Weyl basis
Root systems and Dynkin diagrams
Fundamental weights and representations
Tensor products of representations
Clebsch-Gordan coefficients
Young tableaux and symmetrizers
Casimir operators and invariants
Fermion Fields
Clifford algebras and gamma matrices
Charge conjugation and Majorana conditions
Parity transformation and chiral representations
Spinor bilinears and Fierz identities
Left-handed and right-handed projection operators
CKM matrix and quark mixing
PMNS matrix and neutrino oscillations
Seesaw mechanism for neutrino masses
Higgs Mechanism
Higgs doublet and Higgs potential
Vacuum expectation value (VEV)
Nambu-Goldstone modes
Unitary gauge and physical Higgs boson
Higgs self-couplings and potential parameters
Yukawa matrices and fermion mass terms
Cabibbo-Kobayashi-Maskawa (CKM) matrix
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix
Electroweak Theory
SU(2)L and U(1)Y gauge fields
Gell-Mann-Nishijima formula for electric charge
Neutral currents and GIM mechanism
Weinberg-Salam model and electroweak unification
Gauge boson mass terms and Higgs mechanism
Weinberg angle and Z-boson mass
Fermi constant and W-boson mass
Custodial SU(2) symmetry
Quantum Chromodynamics (QCD)
SU(3) color gauge invariance
Gluon self-interactions and non-Abelian nature
Faddeev-Popov ghosts and BRST symmetry
Running coupling constant and beta function
Asymptotic freedom and infrared slavery
Chiral symmetry breaking and quark condensate
Gluon condensate and vacuum structure
Topological charge and θ-vacuum
Renormalization
Regularization methods (dimensional, Pauli-Villars, lattice)
Minimal subtraction (MS) and modified minimal subtraction (MS-bar) schemes
Counterterms and renormalized Lagrangian
Renormalization group equations (RGEs)
Callan-Symanzik equation
Anomalous dimensions and scaling behavior
Renormalization group fixed points and critical exponents
Universality and renormalization scheme independence
Feynman Diagrams
Feynman rules for propagators and vertices
Feynman parameters and loop integral reduction
Passarino-Veltman reduction and tensor integrals
Dimensional regularization and ε-expansion
One-loop and two-loop diagrams
Higher-order corrections and renormalization
Infrared and collinear divergences
Kinoshita-Lee-Nauenberg theorem and infrared safety
Symmetries and Conservation Laws
Discrete symmetries (C, P, T)
CPT theorem and Lorentz invariance
Global U(1) symmetries and conserved charges
Noether currents and Ward-Takahashi identities
Axial U(1) symmetry and chiral anomaly
Flavor SU(2) and SU(3) symmetries
Isospin and strangeness conservation
Vacuum and Perturbation Theory
Fock space and occupation number representation
Coherent states and squeeze operators
Wick's theorem and contractions
Feynman-Dyson perturbation series
Linked-cluster theorem and connected diagrams
Dyson-Schwinger equations and resummation techniques
Operator product expansion (OPE)
Renormalons and factorial divergences
Functional Methods
Partition function and functional integrals
Schwinger-Dyson equations for Green's functions
Wilsonian renormalization group flow
Effective potential and Coleman-Weinberg mechanism
Background field method and gauge invariance
Functional renormalization group (FRG) approach
Wetterich equation and flow equations
Truncation schemes and approximations
Anomalies
Adler-Bell-Jackiw (ABJ) anomaly
Fujikawa's path integral method
Anomalous Ward identities and BRST symmetry
Wess-Zumino consistency conditions
Descent equations and cohomology
Bardeen's counterterm method
Anomaly matching conditions
't Hooft anomaly matching
Regularization and Renormalization Schemes
Zeta function regularization
Spectral action and noncommutative geometry
Wilsonian renormalization group approach
Polchinski's renormalization group equation
Holographic renormalization and AdS/CFT
Causal perturbation theory and Epstein-Glaser renormalization
BPHZ renormalization scheme
Differential renormalization and coordinate-space methods
Effective Field Theories
Heavy quark effective theory (HQET)
Non-relativistic QCD (NRQCD)
Soft-collinear effective theory (SCET)
Chiral Lagrangians and sigma models
Nambu-Jona-Lasinio (NJL) model
Fermi theory of weak interactions
Euler-Heisenberg Lagrangian for QED
Effective theories for gravity and cosmology
Unitarity and S-matrix
Lehmann-Symanzik-Zimmermann (LSZ) reduction formula
Källén-Lehmann spectral representation
Partial-wave analysis and unitarity bounds
Froissart-Martin bound and high-energy behavior
Regge theory and complex angular momentum
Bootstrap equations and S-matrix theory
Analytic S-matrix and dispersion relations
Finite-energy sum rules and superconvergence
Symmetry Breaking
Goldstone's theorem and Nambu-Goldstone modes
Higgs mechanism and gauge boson masses
Gell-Mann-Oakes-Renner relation for chiral symmetry breaking
Weinberg sum rules for spectral functions
Current algebra and PCAC hypothesis
QCD sum rules and vacuum condensates
Dynamical symmetry breaking and gap equations
Coleman-Mermin-Wagner theorem and lower dimensions
Gauge Fixing and Ghost Fields
Becchi-Rouet-Stora-Tyutin (BRST) symmetry
Faddeev-Popov ghosts and determinant
Nakanishi-Lautrup fields and auxiliary fields
Kugo-Ojima confinement criterion
Gribov ambiguities and Gribov regions
Zwanziger's local horizon condition
Refined Gribov-Zwanziger action
Stochastic quantization and Langevin equation
Quantum Anomalies and Topology
Atiyah-Singer index theorem and Dirac operator
Fujikawa's method and path integral measure
Chern-Simons forms and topological invariants
Wess-Zumino-Witten models and conformal field theory
Chiral anomalies and current algebras
Gauge anomalies and anomaly cancellation
Witten's global anomaly and SU(2) anomaly
Solitons, instantons, and topological charges

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