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Unitary representation

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Summary

A group representation by unitary operators on a Hilbert space.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Notes

For topological groups, continuity is part of the standard analytic notion.

Concept sources

Incoming relations (arrows to this concept)

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Linear representation of a groupUnitary representation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A unitary representation acts by unitary operators on a Hilbert space.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

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Unitary representationOne-particle state

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

One-particle state spaces carry unitary representations of spacetime and internal symmetry groups.

How to interpret this relation type

A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.

Relation sources