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Canonical static concept record

Circle group U(1)U(1)

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Summary

The one-dimensional compact Lie group of complex numbers of unit modulus.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Notes

Isomorphic to R/2πZ\mathbb R/2\pi\mathbb Z and to SO(2)SO(2).

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Compact Lie groupCircle group U(1)U(1)

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

Authored explanation

The circle group is the compact one-dimensional unitary group.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

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Circle group U(1)U(1)Standard Model gauge group

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

Authored explanation

The hypercharge factor is modeled by the circle group.

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.

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