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An associative algebra generated by a quadratic space with .
Sign conventions for and the Clifford relation vary across mathematics and physics.
wp-clifford_algebranlab-clifford_algebraEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A vector space together with a quadratic form canonically determines a new algebra, the quotient of its tensor algebra by the relations . This changes the carrier rather than merely adding data to the vector space.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-clifford_algebranlab-clifford_algebraEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Dirac gamma matrices represent a spacetime Clifford algebra.
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.
wp-physics-dirac_equationnlab-physics-dirac_equationwp-clifford_algebranlab-clifford_algebraThis is an authored directed relation from the source endpoint to the target endpoint.
A chosen representation of the relevant Clifford algebra sends its generators to gamma matrices. The abstract Clifford algebra does not canonically select a particular matrix realization.
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
wp-clifford_algebranlab-clifford_algebrawp-gamma_matricestong-qftThis is an authored directed relation from the source endpoint to the target endpoint.
The spin group is constructed from invertible elements of a Clifford algebra; in Euclidean signature is a double cover, with signature-dependent variants in the indefinite case.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-spin_groupnlab-spin_group