Limitations of a Semiclassical Treatment of the Skyrmion

Braaten, Eric; Ralston, John P.

doi:10.1103/PhysRevD.31.598

Limitations of a Semiclassical Treatment of the Skyrmion

Eric Braaten
(
- Argonne
)
,
John P. Ralston
(
- Argonne and
- Kansas U.
)

Jul, 1984

15 pages

Published in:

Phys.Rev.D 31 (1985) 598

DOI:

10.1103/PhysRevD.31.598

Report number:

ANL-HEP-PR-84-52

View in:

pdf

reference search86 citations

Citations per year

Abstract: (APS)

We discuss a semiclassical approach to the Skyrme model in which the effects from the diagonalization of the collective coordinates are treated in a self-consistent way. We obtain an upper bound on the nucleon-Δ mass difference which is valid if the semiclassical limit is taken with the pion mass parameter held fixed, but is inconsistent with the experimental values of the masses. Because of the interplay of the semiclassical and chiral limits, the approximations break down for sufficiently small pion mass.

Skyrme model
APPROXIMATION: semiclassical
QUANTUM MECHANICS: COLLECTIVE PHENOMENA
FIELD EQUATIONS: SOLITON
FIELD THEORY: EFFECTIVE HAMILTONIANS
MASS DIFFERENCE: (DELTA(1232) NUCLEON)
(DELTA(1232) NUCLEON): MASS DIFFERENCE
PI: MASS
MASS: PI

References(25)

Figures(0)

A Planar Diagram Theory for Strong Interactions

Gerard 't Hooft
(
- CERN
)

- Nucl.Phys.B 72 (1974) 461,
•
DOI:
- 10.1016/0550-3213(74)90154-0

- Nucl.Phys.B 75 41

Baryons in the 1/n Expansion

Edward Witten
(
- Harvard U.
)

- Nucl.Phys.B 160 (1979) 57-115
•
DOI:
- 10.1016/0550-3213(79)90232-3

Global Aspects of Current Algebra

Edward Witten
(
- Princeton U.
)

- Nucl.Phys.B 223 (1983) 422-432,
- IN *SHAPERE, A. (ED.), WILCZEK, F. (ED.): GEOMETRIC PHASES IN PHYSICS* 369-379. (NUCL. PHYS. B223 (1983) 422-432) AND PREPRINT - WITTEN, E. (REC.APR.83) 18 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(83)90063-9

Current Algebra, Baryons, and Quark Confinement

Edward Witten
(
- Princeton U.
)

- Nucl.Phys.B 223 (1983) 433-444,
- In *Rebbi, C. ( Ed.), Soliani, G. ( Ed.): Solitons and Particles*, 617-628. ( Nucl. Phys. B223 ( 1983) 433-444) and Preprint - WITTEN, E. (REC.APR.83) 20p
•
DOI:
- 10.1016/0550-3213(83)90064-0

A Nonlinear field theory

T.H.R. Skyrme
(
- Harwell, AERE
)

- Proc.Roy.Soc.Lond.A 260 (1961) 127-138,
- Also in *Brown, G.E. (ed.): Selected papers of Tony Hilton Royle Skyrme* 195-206
•
DOI:
- 10.1098/rspa.1961.0018

A Unified Field Theory of Mesons and Baryons

T.H.R. Skyrme
(
- Harwell, AERE
)

- Nucl.Phys. 31 (1962) 556-569,
- Also in *Rebbi, C. ( Ed.), Soliani, G. ( Ed.): Solitons and Particles*, 499-512, and in *Lewes 1984, Proceedings, Solitons In Nuclear and Elementary Particle Physics*, 13-26
•
DOI:
- 10.1016/0029-5582(62)90775-7

Kinks and the Dirac equation

T.H.R. Skyrme
(
- Birmingham U.
)

- J.Math.Phys. 12 (1971) 1735-1743,
- Also in *Brown, G.E. (ed.): Selected papers of Tony Hilton Royle Skyrme* 222-230
•
DOI:
- 10.1063/1.1665798

Some Comments on the Many Dimensional Solitons

L.D. Faddeev
(
- CERN and
- Steklov Math. Inst., St. Petersburg
)

- Lett.Math.Phys. 1 (1976) 289
•
DOI:
- 10.1007/BF00398483

Chiral Solitons and Current Algebra

Namik K. Pak
(
- SLAC
)
,
Hsiung Chia Tze
(
- SLAC
)

- Annals Phys. 117 (1979) 164
•
DOI:
- 10.1016/0003-4916(79)90048-4

Exotic Levels from Topology in the QCD Effective Lagrangian

- Phys.Rev.Lett. 49 (1982) 1124,
- Phys.Rev.Lett. 50 (1983) 1630 (erratum)
•
DOI:
- 10.1103/PhysRevLett.49.1124

Soliton States in the QCD Effective Lagrangian

- Phys.Rev.D 27 (1983) 1153,
- Phys.Rev.D 27 (1983) 2772 (erratum)
•
DOI:
- 10.1103/PhysRevD.27.1153

Connection between spin, statistics, and kinks

D. Finkelstein
(
- Yeshiva U.
)
,
J. Rubinstein
(
- Columbia U.
)

- J.Math.Phys. 9 (1968) 1762-1779,
- Also in *Wilczek, F. (ed.): Fractional statistics and anyon superconductivity* 107-124, and in *Kauffman, L.H. (ed.): Knots and applications* 193-210
•
DOI:
- 10.1063/1.1664510