Relativistic Quantum Kinematics in the Moyal Representation

Carinena, Jose F.; Gracia-Bondia, Jose M.; Varilly, Joseph C.

doi:10.1088/0305-4470/23/6/015

Relativistic Quantum Kinematics in the Moyal Representation

Jose F. Carinena
(
- Zaragoza U.
)
,
Jose M. Gracia-Bondia
(
- Costa Rica U.
)
,
Joseph C. Varilly
(
- Costa Rica U.
)

Aug 22, 1989

50 pages

Published in:

J.Phys.A 23 (1990) 901

DOI:

10.1088/0305-4470/23/6/015

Report number:

DFTUZ-89-6

View in:

ADS Abstract Service

reference search42 citations

Citations per year

Abstract: (IOP)

The authors obtain the phase-space quantisation for relativistic spinning particles. The main tool is what they call a 'Stratonovich-Weyl quantiser' which relates functions on phase space to operators on a suitable Hilbert space, and has the essential properties of covariance (under a group representation) and traciality. Their phase spaces are coadjoint orbits of the restricted Poincare group; they compute and explicitly coordinatise the orbits corresponding to massive particles, with or without spin. Some orbits correspond to unitary irreducible representations of the Poincare group; they show that there is a unique Stratonovich-Weyl quantiser from each of these phase spaces to operators on the corresponding representation spaces, and compute it explicitly.

References(38)

Figures(0)

Quantum mechanics as a statistical theory

J.E. Moyal
(
- Queen's U., Belfast
)

- Math.Proc.Cambridge Phil.Soc. 45 (2008) 1, 99-124,
- Proc.Cambridge Phil.Soc. 45 (1949) 99-124,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 9-33
•
DOI:
- 10.1017/S0305004100000487

On the quantum correction for thermodynamic equilibrium

Eugene P. Wigner
(
- Princeton U.
)

- Phys.Rev. 40 (1932) 749-760
•
DOI:
- 10.1103/PhysRev.40.749

On Unitary Representations of the Inhomogeneous Lorentz Group

Eugene P. Wigner
(
- Princeton U.
)

- Annals Math. 40 (1939) 149-204,
- Nucl.Phys.B Proc.Suppl. 6 (1989) 9-64 (reprint)
•
DOI:
- 10.2307/1968551

GROUP THEORETICAL FOUNDATIONS OF CLASSICAL AND QUANTUM MECHANICS. II. ELEMENTARY SYSTEMS

L. Martinez Alonso
(
- Madrid U.
)

- J.Math.Phys. 20 (1979) 219-230
•
DOI:
- 10.1063/1.524068

On the Projective Unitary Representations of Connected Lie Groups

Jose F. Carinena
(
- Valladolid U.
)
,
M. Santander
(
- Valladolid U.
)

- J.Math.Phys. 16 (1975) 1416-1420
•
DOI:
- 10.1063/1.522713

PROJECTIVE COVERING GROUP VERSUS REPRESENTATION GROUPS

Jose F. Carinena
(
- Zaragoza U.
)
,
M. Santander
(
- Valladolid U.
)

- J.Math.Phys. 21 (1980) 440-443,
- J.Math.Phys.21 (1980) 440-443 and Preprint - CARINENA, J. F. (REC.DEC 79) 14p
•
DOI:
- 10.1063/1.524440

The Moyal representation for spin

- Annals Phys. 190 (1989) 107-148
•
DOI:
- 10.1016/0003-4916(89)90262-5

Phase-space representation for Galilean quantum particles of arbitrary spin

- J.Phys.A 21 (1988) L879-L883
•
DOI:
- 10.1088/0305-4470/21/18/002

On Unitary ray representations of continuous groups

V. Bargmann

- Annals Math. 59 (1954) 1-46
•
DOI:
- 10.2307/1969831

- Trans.Am.Math.Soc. 212 113

- Bull.Soc.Math.Fr. 100 301

- Sov.Phys.JETP 31 1012

Parity Operator and Quantization of Delta Functions

A. Grossmann
(
- Marseille, CPT
)

- Commun.Math.Phys. 48 (1976) 191,
- Commun.Math.Phys.48 (1976) 191-194 and Marseille Centre Phys Theor - 75-P.763 (75,REC.NOV) 8p
•
DOI:
- 10.1007/BF01617867

Wigner function as the expectation value of a parity operator

Antoine Royer
(
- Unlisted
)

- Phys.Rev.A 15 (1977) 449-450
•
DOI:
- 10.1103/PhysRevA.15.449

Classical lorentz invariant particles

R. Arens
(
- UCLA
)

- J.Math.Phys. 12 (1971) 2415-2422
•
DOI:
- 10.1063/1.1665553

Canonical Realizations of the Poincare Group. 1. General Theory

M. Pauri
(
- Parma U.
)
,
G.M. Prosperi
(
- Milan U.
)

- J.Math.Phys. 16 (1975) 1503-1521
•
DOI:
- 10.1063/1.522701

- Ann.Inst.H.Poincare Phys.Theor.A 33 409

On the Relation Between Momentum and Velocity for Elementary Systems

- Phys.Lett.A 61 (1977) 353
•
DOI:
- 10.1016/0375-9601(77)90329-2

Localized States for Elementary Systems

T.D. Newton
(
- Princeton U.
)
,
Eugene P. Wigner
(
- Princeton U.
)

- Rev.Mod.Phys. 21 (1949) 400-406,
- Reprinted in *Noz, M.E. (ed.), Kim, Y.S. (ed.): Special relativity and quantum theory* 395-401
•
DOI:
- 10.1103/RevModPhys.21.400

Remark on Causality and Particle Localization

Gerhard C. Hegerfeldt
(
- Heidelberg U.
)

- Phys.Rev.D 10 (1974) 3320
•
DOI:
- 10.1103/PhysRevD.10.3320

On Newton-wigner Localization and Superluminal Propagation Speeds

S.N.M. Ruijsenaars
(
- Munich, Max Planck Inst.
)

- Annals Phys. 137 (1981) 33
•
DOI:
- 10.1016/0003-4916(81)90059-2

VIOLATION OF CAUSALITY IN RELATIVISTIC QUANTUM THEORY?

Gerhard C. Hegerfeldt
(
- Gottingen U. and
- Caltech
)

- Phys.Rev.Lett. 54 (1985) 2395
•
DOI:
- 10.1103/PhysRevLett.54.2395

- Fortsch.Phys. 11 863

- J.Phys.A 22 1

Relativistic Quantum Transport Theory Approach to Multiparticle Production

P. Carruthers
(
- Los Alamos
)
,
F. Zachariasen
(
- Caltech
)

- Phys.Rev.D 13 (1976) 950
•
DOI:
- 10.1103/PhysRevD.13.950

1-25 of 38
1
2
25 / page