title: List of mathematical topics in quantum theory
text: # 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
  