Abstract
The graded extension of the de Sitter space-time algebra so(3,2) is identical to the structure defined by polynomials of order 1 and 2 in the natural coordinates of four-dimensional phase space. Ordinary Weyl quantization gives a representation that is unique among all the representations of the graded algebra in that the Poisson bracket relations (which are not part of the structure of the graded algebra) are preserved. The restriction of this representation to the Lie subalgebra so(3,2) is the direct sum Di ⊕ Rac of the two singleton representations. There exists a unique, supersymmetric, interacting field theory of a single Dirac multiplet. The interaction Lagrangian has the form , where is the scalar Rac field, and are the spinor Di "field strength" and associated "potential," and is a real coupling constant. Applications to confinement and to composite massless particles is discussed.
- Received 10 August 1981
DOI:https://doi.org/10.1103/PhysRevD.26.1988
©1982 American Physical Society