Spin statistics theorem and scattering in planar quantum field theories with braid statistics

Frohlich, J.; Marchetti, P.A.

doi:10.1016/0550-3213(91)90378-B

Spin statistics theorem and scattering in planar quantum field theories with braid statistics

J. Frohlich
(
- Zurich, ETH
)
,
P.A. Marchetti
(
- Padua U. and
- INFN, Padua
)

May, 1990

41 pages

Published in:

Nucl.Phys.B 356 (1991) 533-573

Published: 1991

DOI:

10.1016/0550-3213(91)90378-B

Report number:

DFPD-90-TH-10

View in:

AMS MathSciNet

reference search69 citations

Citations per year

Abstract: (Elsevier)

We further develop the general theory of superselection sectors and their statistics for quantum fields on three-dimensional space-time. We show that the statistics of particles that are not localizable in bounded regions of space-time (but in space-like cones) are described by braid-group, rather than permutation-group representations, unless their spins are integral or half-integral. A general connection between spin and statistics is established. Extensions of the theory to non-relativistic systems of two-dimensional condensed matter physics are sketched which makes it applicable to the fractional quantum Hall effect and certain models of high- T c superconductivity.

axiomatic field theory: superselection rule
field theory: planar
spin: statistics
statistics: spin
dimension: 3
braid group: representation
Hall effect: fractional
postulated particle: anyon
scattering: anyon
anyon: scattering

References(36)

Figures(0)

Irreducible unitary representations of the Lorentz group

V. Bargmann
(
- Princeton, Inst. Advanced Study
)

- Annals Math. 48 (1947) 568-640
•
DOI:
- 10.2307/1969129

Magnetic Flux, Angular Momentum, and Statistics

Frank Wilczek
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 48 (1982) 1144-1146
•
DOI:
- 10.1103/PhysRevLett.48.1144

Quantum Mechanics of Fractional Spin Particles

Frank Wilczek
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 49 (1982) 957-959
•
DOI:
- 10.1103/PhysRevLett.49.957

On the theory of identical particles

J.M. Leinaas
(
- Oslo U.
)
,
J. Myrheim
(
- Oslo U.
)

- Nuovo Cim.B 37 (1977) 1-23,
- Reprinted in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 132-154
•
DOI:
- 10.1007/BF02727953

Quantum Field Theory of Anyons

J. Frohlich
(
- Zurich, ETH
)
,
P.A. Marchetti
(
- Padua U. and
- INFN, Padua
)

- Lett.Math.Phys. 16 (1988) 347
•
DOI:
- 10.1007/BF00402043

Quantum Field Theories of Vortices and Anyons

J. Frohlich
(
- Zurich, ETH
)
,
P.A. Marchetti
(
- Padua U. and
- INFN, Padua
)

- Commun.Math.Phys. 121 (1989) 177-223,
- COMMUN. MATH. PHYS. 121 (1989) 177-223 AND PREPRINT - FROEHLICH, J. (REC.AUG.88) 78p
•
DOI:
- 10.1007/BF01217803

Locality and the Structure of Particle States

Detlev Buchholz
(
- Hamburg U.
)
,
Klaus Fredenhagen
(
- Freiburg U.
)

- Commun.Math.Phys. 84 (1982) 1
•
DOI:
- 10.1007/BF01208370

Bosonization in (2+1)-Dimensions

M. Luscher
(
- DESY
)

- Nucl.Phys.B 326 (1989) 557-582
•
DOI:
- 10.1016/0550-3213(89)90544-0

Exotic Spin and Statistics in (2+1)-Dimensional Canonical Quantum Field Theory

Gordon W. Semenoff
(
- British Columbia U.
)
,
Pasquale Sodano
(
- Los Alamos
)

- Nucl.Phys.B 328 (1989) 753-776
•
DOI:
- 10.1016/0550-3213(89)90229-0

Off diagonal long range order, oblique confinement, and the fractional quantum Hall effect

S.M. Girvin
(
- NIST, Wash., D.C.
)
,
A.H. MacDonald
(
- CRPP, Ottawa
)

- Phys.Rev.Lett. 58 (1987) 1252-1255,
- Reprinted in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 258-261
•
DOI:
- 10.1103/PhysRevLett.58.1252

- Phys.Rev.Lett. 61 86

Topologically Massive Gauge Theories

- Annals Phys. 140 (1982) 372-411,
- Annals Phys. 185 (1988) 406 (erratum),
- Annals Phys. 281 (2000) 409-449
•
DOI:
- 10.1016/0003-4916(82)90164-6

Superselection Sectors with Braid Group Statistics and Exchange Algebras. 1. General Theory

K. Fredenhagen
(
- Freie U., Berlin
)
,
Karl-Henning Rehren
(
- Freie U., Berlin
)
,
B. Schroer
(
- Freie U., Berlin
)

- Commun.Math.Phys. 125 (1989) 201
•
DOI:
- 10.1007/BF01217906

Anomalous quantum Hall effect: An Incompressible quantum fluid with fractionallycharged excitations

R.B. Laughlin
(
- LLNL, Livermore
)

- Phys.Rev.Lett. 50 (1983) 1395,
•
DOI:
- 10.1103/PhysRevLett.50.1395

Statistics of quasiparticles and the hierarchy of fractional quantized Hall states

B.I. Halperin
(
- Harvard U.
)

- Phys.Rev.Lett. 52 (1984) 1583-1586,
- Phys.Rev.Lett. 52 (1984) 2390 (erratum)
•
DOI:
- 10.1103/PhysRevLett.52.1583

Statistics of quasiparticles and the hierarchy of fractional quantized Hall states

B.I. Halperin
(
- Harvard U.
)

- Phys.Rev.Lett. 52 (1984) 1583-1586,
- Phys.Rev.Lett. 52 (1984) 2390 (erratum)
•
DOI:
- 10.1103/PhysRevLett.52.1583

Composite fermion approach for the fractional quantum Hall effect

J.K. Jain
(
- Yale U.
)

- Phys.Rev.Lett. 63 (1989) 199-202
•
DOI:
- 10.1103/PhysRevLett.63.199

Equivalence of the resonating valence bond and fractional quantum Hall states

V. Kalmeyer
(
- Stanford U., Phys. Dept. and
- LLNL, Livermore
)
,
R.B. Laughlin
(
- Stanford U., Phys. Dept. and
- LLNL, Livermore
)

- Phys.Rev.Lett. 59 (1987) 2095-2098,
- Reprinted in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 308-311
•
DOI:
- 10.1103/PhysRevLett.59.2095

Random phase approximation in the fractional statistics gas

A.L. Fetter
(
- Stanford U., Phys. Dept. and
- LLNL, Livermore
)
,
C.B. Hanna
(
- Stanford U., Phys. Dept. and
- LLNL, Livermore
)
,
R.B. Laughlin
(
- Stanford U., Phys. Dept. and
- LLNL, Livermore
)

- Phys.Rev.B 39 (1989) 9679-9681,
- Reprinted in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 339-341
•
DOI:
- 10.1103/PhysRevB.39.9679

On Anyon Superconductivity

- Int.J.Mod.Phys.B 3 (1989) 1001,
•
DOI:
- 10.1142/S0217979289000725

An Algebraic approach to quantum field theory

- J.Math.Phys. 5 (1964) 848-861
•
DOI:
- 10.1063/1.1704187

Local observables and particle statistics. 1

Sergio Doplicher
(
- Marseille U., Luminy
)
,
Rudolf Haag
(
- Hamburg U.
)
,
John E. Roberts
(
- Princeton U.
)

- Commun.Math.Phys. 23 (1971) 199-230
•
DOI:
- 10.1007/BF01877742

Local observables and particle statistics. 2

- Commun.Math.Phys. 35 (1974) 49-85
•
DOI:
- 10.1007/BF01646454

Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics

S. Doplicher
(
- Rome U.
)
,
J.E. Roberts
(
- Osnabruck U.
)

- Commun.Math.Phys. 131 (1990) 51-107
•
DOI:
- 10.1007/BF02097680

Charged Sectors and Scattering States in Quantum Electrodynamics

J. Frohlich
(
- IHES, Bures-sur-Yvette
)
,
G. Morchio
(
- Pisa U.
)
,
F. Strocchi
(
- CERN
)

- Annals Phys. 119 (1979) 241-248
•
DOI:
- 10.1016/0003-4916(79)90187-8

1-25 of 36
1
2
25 / page