On free massless (pseudo)scalar quantum field theory in (1+1)-dimensional space-time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that a continuous symmetry of (pseudo)scalar field translations is spontaneously broken. Goldstone bosons appear as quanta of a free massless (pseudo)scalar field. We show that the main inequality between vacuum expectation values of certain operators which has been used for the derivation of the Mermin-Wagner-Hohenberg theorem is fulfilled in the quantum field theory of a free massless (pseudo)scalar field free of infrared divergences.

Note:

20 pages, Latex, no figures, the manuscript is revised according to the version accepted for publication in EPJC

field theory: scalar
massless
dimension: 2
field theory: pseudoscalar
spontaneous symmetry breaking
Goldstone particle
random field
correlation function
infrared problem
coherent state

References(16)

Figures(0)

A Soluble relativistic field theory?

Walter E. Thirring
(
- Washington U., Seattle
)

- Annals Phys. 3 (1958) 91-112,
•
DOI:
- 10.1016/0003-4916(58)90015-0

- Nuovo Cim. 9 1007

An explicit solution of the Thirring model

V. Glaser
(
- CERN
)

- Nuovo Cim. 9 (1958) 6, 990-1006
•
DOI:
- 10.1007/BF02777950

There are no Goldstone bosons in two-dimensions

Sidney R. Coleman
(
- Princeton U.
)

- Commun.Math.Phys. 31 (1973) 259-264
•
DOI:
- 10.1007/BF01646487

On the equivalence between Sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

Manfried Faber
(
- Vienna, Tech. U., Atominst. and
- Vienna, Tech. U.
)
,
A.N. Ivanov
(
- Vienna, Tech. U., Atominst. and
- Vienna, Tech. U.
)

- Eur.Phys.J.C 20 (2001) 723-757
•
e-Print:
- hep-th/0105057
•
DOI:
- 10.1007/s100520100694

Field Theories with Superconductor Solutions

J. Goldstone
(
- CERN
)

- Nuovo Cim. 19 (1961) 154-164,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 93-103
•
DOI:
- 10.1007/BF02812722

Broken Symmetries

Jeffrey Goldstone
(
- Cambridge U.
)
,
Abdus Salam
(
- Imperial Coll., London
)
,
Steven Weinberg
(
- Imperial Coll., London
)

- Phys.Rev. 127 (1962) 965-970,
- Also in *Lai, C. H. ( Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 118-123,
- Also in *Ali, A. (ed.) et al.: Selected papers of Abdus Salam* 204-209
•
DOI:
- 10.1103/PhysRev.127.965

On the solution of the massless Thirring model with fermion fields quantized in the chiral symmetric phase

Manfried Faber
(
- Vienna, Tech. U., Atominst. and
- Vienna, Tech. U.
)
,
A.N. Ivanov
(
- Vienna, Tech. U., Atominst. and
- Vienna, Tech. U.
)

e-Print:
- hep-th/0112183

The Quantum Sine-Gordon Equation as the Massive Thirring Model

Sidney R. Coleman
(
- Harvard U.
)

- Phys.Rev.D 11 (1975) 2088,
•
DOI:
- 10.1103/PhysRevD.11.2088

A Nonlinear theory of strong interactions

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

- Proc.Roy.Soc.Lond.A 247 (1958) 260-278,
- Also in *Brown, G.E. (ed.): Selected papers of Tony Hilton Royle Skyrme* 166-184
•
DOI:
- 10.1098/rspa.1958.0183

- Phys.Rev.A 262 237

Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models

N.D. Mermin
(
- Cornell U., LNS
)
,
H. Wagner
(
- Cornell U., LNS
)

- Phys.Rev.Lett. 17 (1966) 1133-1136
•
DOI:
- 10.1103/PhysRevLett.17.1133

Existence of Long-Range Order in One and Two Dimensions

P.C. Hohenberg
(
- Bell Labs
)

- Phys.Rev. 158 (1967) 383-386
•
DOI:
- 10.1103/PhysRev.158.383

- J.Math.Phys. 8 1061

Microscopic theory of superconductivity

John Bardeen
(
- Illinois U., Urbana
)
,
L.N. Cooper
(
- Illinois U., Urbana
)
,
J.R. Schrieffer
(
- Illinois U., Urbana
)

- Phys.Rev. 106 (1957) 162
•
DOI:
- 10.1103/PhysRev.106.162

Theory of superconductivity

John Bardeen
(
- Illinois U., Urbana
)
,
L.N. Cooper
(
- Illinois U., Urbana
)
,
J.R. Schrieffer
(
- Illinois U., Urbana
)

- Phys.Rev. 108 (1957) 1175-1204
•
DOI:
- 10.1103/PhysRev.108.1175