# List of mathematical topics in quantum theory

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