# Category: Theorems in quantum mechanics

Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix (S-matrix) are free of ultraviolet divergencies. Green's
Gell-Mann and Low theorem
The Gell-Mann and Low theorem is a theorem in quantum field theory that allows one to relate the ground (or vacuum) state of an interacting system to the ground state of the corresponding non-interact
Nielsen–Ninomiya theorem
In lattice field theory, the Nielsen–Ninomiya theorem is a no-go theorem about placing chiral fermions on the lattice. In particular, under very general assumptions such as locality, hermiticity, and
The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical system remains in its instantaneous eigenstate i
Haag's theorem
While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now common
Ehrenfest theorem
The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators
Hellmann–Feynman theorem
In quantum mechanics, the Hellmann–Feynman theorem relates the derivative of the total energy with respect to a parameter, to the expectation value of the derivative of the Hamiltonian with respect to
Solèr's theorem
In mathematics, Solèr's theorem is a result concerning certain infinite-dimensional vector spaces. It states that any orthomodular form that has an infinite orthonormal sequence is a Hilbert space ove
PBR theorem
The PBR theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named) in 2012. It has particular significance for how one
No-deleting theorem
In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of
Landau–Yang theorem
In quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle with spin 1 cannot decay into two photo
Bell's theorem
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories given some basic
Levinson's theorem
Levinson's theorem is an important theorem in non-relativistic quantum scattering theory. It relates the number of bound states of a potential to the difference in phase of a scattered wave at zero an
No-cloning theorem
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the fi
Wigner–Eckart theorem
The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be
Runge–Gross theorem
In quantum mechanics, specifically time-dependent density functional theory, the Runge–Gross theorem (RG theorem) shows that for a many-body system evolving from a given initial wavefunction, there ex
CPT symmetry
Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T)
Furry's theorem
In quantum electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines connected to an odd number of vertices, its contribution vanishes. As a corollar
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Vafa–Witten theorem
In theoretical physics, the Vafa–Witten theorem, named after Cumrun Vafa and Edward Witten, is a theorem that shows that vector-like global symmetries (those that transform as expected under reflectio
Byers–Yang theorem
In quantum mechanics, the Byers–Yang theorem states that all physical properties of a doubly connected system (an annulus) enclosing a magnetic flux through the opening are periodic in the flux with p
Optical equivalence theorem
The optical equivalence theorem in quantum optics asserts an equivalence between the expectation value of an operator in Hilbert space and the expectation value of its associated function in the phase
Kramers' theorem
In quantum mechanics, the Kramers' degeneracy theorem states that for every energy eigenstate of a time-reversal symmetric system with half-integer total spin, there is another eigenstate with the sam
Weinberg–Witten theorem
In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin j > 1/2 cannot carry a
Wigner's theorem
Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical symmetries such as rotations, translations,
Kato theorem
The Kato theorem, or Kato's cusp condition (after Japanese mathematician Tosio Kato), is used in computational quantum physics. It states that for generalized Coulomb potentials, the electron density
Haag–Łopuszański–Sohnius theorem
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only way to nontrivially mix spacetime and internal
Mermin–Wagner theorem
In quantum field theory and statistical mechanics, the Mermin–Wagner theorem (also known as Mermin–Wagner–Hohenberg theorem, Mermin–Wagner–Berezinskii theorem, or Coleman theorem) states that continuo
Elitzur's theorem
In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant und
Reeh–Schlieder theorem
The Reeh–Schlieder theorem is a result in relativistic local quantum field theory published by and (1918-2003) in 1961. The theorem states that the vacuum state is a cyclic vector for the field algebr
Kinoshita–Lee–Nauenberg theorem
The Kinoshita–Lee–Nauenberg theorem or KLN theorem states that perturbatively the standard model as a whole is infrared (IR) finite. That is, the infrared divergences coming from loop integrals are ca
In physics, the no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning theorem for pure stat
Cluster decomposition
In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum exp
Coleman–Mandula theorem
In theoretical physics, the Coleman–Mandula theorem is a no-go theorem stating that spacetime and internal symmetries can only combine in a trivial way. This means that the charges associated with int
Spin–statistics theorem
In quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle (angular momentum not due to the orbital motion) to the particle statistics it obeys. In units of the reduced
No-hiding theorem
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and
Kochen–Specker theorem
In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 19
C-theorem
In quantum field theory the C-theorem states that there exists a positive real function, , depending on the coupling constants of the quantum field theory considered, , and on the energy scale, , whic
No-communication theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not pos