TL;DR
This paper explores the affine symmetry group in higher-dimensional spacetime, introducing infinite-dimensional spinorial representations and a Dirac-like equation with generalized gamma matrices.
Contribution
It presents the first construction of infinite-dimensional spinorial representations and a Dirac-like equation for the affine symmetry group in D ≥ 3 dimensions.
Findings
Infinite-dimensional spinorial representations are developed.
A Dirac-like affine equation with generalized gamma matrices is formulated.
The affine symmetry group is covered in higher-dimensional spacetime.
Abstract
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are presented. A Dirac-like affine equation, with infinite matrices generalizing the matrices, is constructed.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Cosmology and Gravitation Theories