List of mathematical topics in quantum theory explained

This is a list of mathematical topics in quantum theory, by Wikipedia page. See also list of functional analysis topics, list of Lie group topics, list of quantum-mechanical systems with analytical solutions.

Mathematical formulation of quantum mechanics

• bra–ket notation
• canonical commutation relation
• complete set of commuting observables
• Heisenberg picture
• Hilbert space
• Interaction picture
• Measurement in quantum mechanics
• quantum field theory
• quantum logic
• quantum operation
• Schrödinger picture
• semiclassical
• statistical ensemble
• wavefunction
• wave–particle duality
• Wightman axioms
• WKB approximation

Schrödinger equation

• quantum mechanics, matrix mechanics, Hamiltonian (quantum mechanics)
• particle in a box
• particle in a ring
• particle in a spherically symmetric potential
• quantum harmonic oscillator
• hydrogen atom
• ring wave guide
• particle in a one-dimensional lattice (periodic potential)
• Fock symmetry in theory of hydrogen

Symmetry

• identical particles
• angular momentum
  • angular momentum operator
• rotational invariance
  • rotational symmetry
  • rotation operator
• translational symmetry
• Lorentz symmetry
• Parity transformation
• Noether's theorem
• Noether charge
• Spin (physics)
  • isospin
• Aman matrices
• scale invariance
• spontaneous symmetry breaking
• supersymmetry breaking

Quantum states

• quantum number
• Pauli exclusion principle
• quantum indeterminacy
• uncertainty principle
• wavefunction collapse
• zero-point energy
• bound state
• coherent state
  • squeezed coherent state
• density state
• Fock state, Fock space
• vacuum state
• quasinormal mode
• no-cloning theorem
• quantum entanglement

Dirac equation

• spinor, spinor group, spinor bundle
• Dirac sea
• Spin foam
• Poincaré group
• gamma matrices
• Dirac adjoint
• Wigner's classification
• anyon

Interpretations of quantum mechanics

• Copenhagen interpretation
• locality principle
• Bell's theorem
  • Bell test loopholes
• CHSH inequality
• hidden variable theory
• path integral formulation, quantum action
• Bohm interpretation
• many-worlds interpretation
• Tsirelson's bound

Quantum field theory

• Feynman diagram
  • One-loop Feynman diagram
• Schwinger's quantum action principle
• Propagator
• Annihilation operator
• S-matrix
• Standard Model
• Local quantum physics
• Nonlocal
• Effective field theory
• Correlation function (quantum field theory)
• Renormalizable
• Cutoff
• Infrared divergence, infrared fixed point
• Ultraviolet divergence
• Fermi's interaction
• Path-ordering
• Landau pole
• Higgs mechanism
• Wilson line
• Wilson loop
• Tadpole (physics)
• Lattice gauge theory
• BRST charge
• Anomaly (physics)
• Chiral anomaly
• Braid statistics
• Plekton

Computation

• quantum computing
• qubit
• qutrit
• pure qubit state
• quantum dot
• Kane quantum computer
• quantum cryptography
• quantum decoherence
• quantum circuit
• universal quantum computer
• measurement based Quantum Computing
• timeline of quantum computing

Supersymmetry

• Lie superalgebra
• supergroup (physics)
• supercharge
• supermultiplet
• supergravity

Quantum gravity

• theory of everything
• loop quantum gravity
• spin network
• black hole thermodynamics

Non-commutative geometry

• Quantum group
• Hopf algebra
• Noncommutative quantum field theory

String theory

See list of string theory topics

• Matrix model