nLab
Wigner theorem

not to be confused with Wigner classification

Context

AQFT

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Concepts

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Theorems

States and observables

Operator algebra

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Local QFT

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Perturbative QFT

Contents

Statement

Wigner’s theorem asserts that a function f:HHf : H \to H from a Hilbert space to itself (not assumed to be a linear function)
is linear and in fact a (anti-)unitary operator (up to a phase) if only the function is

  1. surjective;

  2. norm-preserving.

Role in quantum mechanics

In quantum mechanics every symmetric operation needs to be a norm-preserving bijection from a Hilbert space of states to itself. Hence Wigner’s theorem asserts that in quantum mechanics symmetries are presented by unitary operators (or more rarely anti-unitary operator?s, as for example time reversal?).

Other theorems about the foundations and interpretation of quantum mechanics include:

References

See also

Last revised on December 28, 2017 at 17:36:57. See the history of this page for a list of all contributions to it.