# Quantum algebra of superspace

## Abstract

We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.

- Authors:

- Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas 1080A (Venezuela)

- Publication Date:

- OSTI Identifier:
- 20776805

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.046008; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; ANGULAR MOMENTUM; CHIRAL SYMMETRY; CHIRALITY; COMMUTATORS; HILBERT SPACE; IRREDUCIBLE REPRESENTATIONS; MATHEMATICAL SOLUTIONS; QUANTIZATION; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SPACE-TIME; SUPERSYMMETRY; TENSORS; WAVE FUNCTIONS

### Citation Formats

```
Hatcher, N., Restuccia, A., and Stephany, J.
```*Quantum algebra of superspace*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.046008.

```
Hatcher, N., Restuccia, A., & Stephany, J.
```*Quantum algebra of superspace*. United States. doi:10.1103/PhysRevD.73.046008.

```
Hatcher, N., Restuccia, A., and Stephany, J. Wed .
"Quantum algebra of superspace". United States.
doi:10.1103/PhysRevD.73.046008.
```

```
@article{osti_20776805,
```

title = {Quantum algebra of superspace},

author = {Hatcher, N. and Restuccia, A. and Stephany, J.},

abstractNote = {We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.},

doi = {10.1103/PhysRevD.73.046008},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}