Fields on the Poincare group: Arbitrary spin description and relativistic wave equations

In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered as generating functions for conventional spin-tensor fields. The cases of 2, 3, and 4 dimensions are elaborated in detail. Discrete transformations

C,P,T

are defined for the scalar fields as automorphisms of the Poincare group. Doing a classification of the scalar functions, we obtain relativistic wave equations for particles with definite spin and mass. There exist two different types of scalar functions (which describe the same mass and spin), one related to a finite-dimensional nonunitary representation and another one related to an infinite-dimensional unitary representation of the Lorentz subgroup. This allows us to derive both usual finite-component wave equations for spin-tensor fields and positive energy infinite-component wave equations.

group theory: Poincare
group theory: geometrical
group theory: representation
field equations
spin: high
dimension: 2-4
field theory: scalar
bibliography

References(90)

Figures(0)

On relativistic wave equations for particles of arbitrary spin in an electromagnetic field

M. Fierz
(
- Zurich, ETH
)
,
W. Pauli
(
- Zurich, ETH
)

- Proc.Roy.Soc.Lond.A 173 (1939) 211-232
•
DOI:
- 10.1098/rspa.1939.0140

Lagrangian formulation for arbitrary spin. 1. The boson case

L.P.S. Singh
(
- Rochester U.
)
,
C.R. Hagen
(
- Rochester U.
)

- Phys.Rev.D 9 (1974) 898-909
•
DOI:
- 10.1103/PhysRevD.9.898

Lagrangian formulation for arbitrary spin. 2. The fermion case

L.P.S. Singh
(
- Rochester U.
)
,
C.R. Hagen
(
- Rochester U.
)

- Phys.Rev.D 9 (1974) 910-920
•
DOI:
- 10.1103/PhysRevD.9.910

Relativistic wave equations for particles with arbitrary spin

W.J. Hurley
(
- Syracuse U.
)

- Phys.Rev.D 4 (1971) 3605-3616
•
DOI:
- 10.1103/PhysRevD.4.3605

Pair production and solutions of the wave equation for particles with arbitrary spin

S.I. Kruglov
(
- Intl. Educ. Ctr., Toronto
)

•
e-Print:
- hep-ph/9908410

Sur la theorie des particules élémentaires de spin quelconque. I

J.K. Lubański

- Physica 9 (1942) 3, 310-324
•
DOI:
- 10.1016/s0031-8914(42)90113-7

Relativistic Wave Equations for the Elementary Particles

H.J. Bhabha
(
- Tata Inst.
)

- Rev.Mod.Phys. 17 (1945) 200-216
•
DOI:
- 10.1103/RevModPhys.17.200

Bhabha First Order Wave Equations. 7. Summary and Conclusions

- Phys.Rev.D 15 (1977) 445
•
DOI:
- 10.1103/PhysRevD.15.445

Relativistic theory of particles with arbitrary intrinsic angular momentum

Ettore Majorana
(
- Rome U.
)

- Nuovo Cim. 9 (1932) 335-344
•
DOI:
- 10.1007/BF02959557

Majorana representations of the Lorentz group and infinite component fields

D.Ts. Stoyanov
(
- Dubna, JINR
)
,
I.T. Todorov
(
- ICTP, Trieste
)

- J.Math.Phys. 9 (1968) 2146-2167
•
DOI:
- 10.1063/1.1664556

A positive-energy relativistic wave equation

P.A.M. Dirac
(
- Florida State U.
)

- Proc.Roy.Soc.Lond.A 322 (1971) 435-445
•
DOI:
- 10.1098/rspa.1971.0077

A positive-energy relativistic wave equation. 2.

P.A.M. Dirac
(
- Florida State U.
)

- Proc.Roy.Soc.Lond.A 328 (1972) 1-7,
- Proc. Roy. Soc. (London) Ser. A 328 (1972) 1-7
•
DOI:
- 10.1098/rspa.1972.0064

Relativistic wave equations for anyons

R. Jackiw
(
- MIT, LNS
)
,
V.P. Nair
(
- Columbia U.
)

- Phys.Rev.D 43 (1991) 1933-1942
•
DOI:
- 10.1103/PhysRevD.43.1933

The model of a free relativistic particle with fractional spin

M.S. Plyushchay
(
- Serpukhov, IHEP
)

- Int.J.Mod.Phys.A 7 (1992) 7045-7064
•
DOI:
- 10.1142/S0217751X92003239

Anyons as spinning particles

Jose L. Cortes
(
- Zaragoza U.
)
,
Mikhail S. Plyushchay
(
- Zaragoza U.
)

- Int.J.Mod.Phys.A 11 (1996) 3331-3362
•
e-Print:
- hep-th/9505117
•
DOI:
- 10.1142/S0217751X96001590

Poincare group and relativistic wave equations in (2+1)-dimensions

D.M. Gitman
(
- Sao Paulo U.
)
,
A.L. Shelepin
(
- Moscow, Radiotech. Inst.
)

- J.Phys.A 30 (1997) 6093-6121
•
DOI:
- 10.1088/0305-4470/30/17/018

Relativistic wave equations

Paul A.M. Dirac
(
- Cambridge U.
)

- Proc.Roy.Soc.Lond.A 155 (1936) 447-459
•
DOI:
- 10.1098/rspa.1936.0111

On a theory of particles with half integral spin

William Rarita
(
- UC, Berkeley
)
,
Julian Schwinger
(
- UC, Berkeley
)

- Phys.Rev. 60 (1941) 61
•
DOI:
- 10.1103/PhysRev.60.61

Group Theoretical Discussion of Relativistic Wave Equations

V. Bargmann
(
- Princeton U.
)
,
Eugene P. Wigner
(
- Princeton U.
)

- Proc.Nat.Acad.Sci. 34 (1948) 211,
- Reprinted in *Noz, M.E. (ed.), Kim, Y.S. (ed.): Special relativity and quantum theory* 103-117
•
DOI:
- 10.1073/pnas.34.5.211

The particle aspect of meson theory

N. Kemmer

- Proc.Roy.Soc.Lond.A 173 (1939) 91-116
•
DOI:
- 10.1098/rspa.1939.0131

On Relativistic Wave Equations

Harish-Chandra
(
- Cambridge U.
)

- Phys.Rev. 71 (1947) 793-805
•
DOI:
- 10.1103/PhysRev.71.793

General relativistically invariant equations and infinite-dimensional representations of the Lorentz group

- Zh.Eksp.Teor.Fiz. 18 (1948) 8, 703-733

- Zh.Eksp.Teor.Fiz. 17 227

- Acta Phys.Polon. 15 163

More on equations of motion for interacting massless fields of all spins in (3+1)-dimensions

Mikhail A. Vasiliev
(
- Goteborg, ITP
)

- Phys.Lett.B 285 (1992) 225-234,
- Phys. Lett. B285 (1992) 225-234 and Goeteborg Chalmers Univ. Technol. - 92-06 (92/02,rec.Feb.) 14 p. (203695)
•
DOI:
- 10.1016/0370-2693(92)91457-K

1-25 of 90
1
2
3
4
25 / page