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Integrable quantum field theories and Bogoliubov transformations
ANNALS
OF PHYSICS
132,235-236
Abstracts
First
Order
DANIEL
Transitions
(1981)
of Papers
Induced
by Fluctuations
to Appear
in General
in Future
@Theories.
Issues
HADASA
H.
IACOBSON
AND
J. AMIT. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel.
Generalizing arguments introduced to study the critical properties of n-component theories with and arguments used to study the first order transition in systems with cubic coupling gijrdikbdl, anisotropy, it is shown that, if there is more than one invariant in the interaction, then (a) every such system has a domain of “runaway” trajectories in coupling constant space, (b) a first order transition can then be exhibited in a systematic expansion in s (=4 - d). The arguments are also explicitly exhibited for the system with a quartic anisotropy having the Potts symmetry.
Quantum Field Theories and Bogoliubou Transformations. S. N. M. RUIJSENAARS.Department of Physics, Princeton University, Princeton, New Jersey 08544.
Integrable
The Federbush, massless Thirring and continuum lsing models and related integrable relativistic quantum field theories are studied. It is shown that local and covariant classical field operators exist that generate Bogoliubov transformations of the annihilation and creation operators on the Fock spaces of the respective models. The quantum fields of these models are closely related or equal to quadratic forms implementing these transformations, and hence formally inherit the covariance and locality of the underlying classical field operators. It is proved that the Federbush and massless Thirring fields on the physical sector do not satisfy the equation of motion. Closely related fields are defined that do satisfy it, and which lead to the same S-matrix, but these fields are presumably nonlocal. Bethe transforms are constructed for the various models, and on the unphysical sector the relation with the field theory approach is established.
Analysis in Field Theory. P. M. STEVENSON.Physics Department, University of WisconsinMadison, Madison, Wisconsin 53706.
Dimensional
Dimensional Transmutation (the breakdown of scale invariance in field theories) is reconciled with the commonsense notions of Dimensional Analysis. This makes possible a discussion of the meaning of the Renormalisation Group equations, completely divorced from the technicalities of renormalisation. As illustrations, I describe some very familiar QCD results in these terms.
The Gauge
Transformations
Physique Theorique,
of the Schwinger Model. A. K. RAINA AND Universite de Lausanne, Lausanne, Switzerland.
G. WANDERS. Institut de
We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model’s vacuum structure. 235 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.
OF PHYSICS
132,235-236
Abstracts
First
Order
DANIEL
Transitions
(1981)
of Papers
Induced
by Fluctuations
to Appear
in General
in Future
@Theories.
Issues
HADASA
H.
IACOBSON
AND
J. AMIT. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel.
Generalizing arguments introduced to study the critical properties of n-component theories with and arguments used to study the first order transition in systems with cubic coupling gijrdikbdl, anisotropy, it is shown that, if there is more than one invariant in the interaction, then (a) every such system has a domain of “runaway” trajectories in coupling constant space, (b) a first order transition can then be exhibited in a systematic expansion in s (=4 - d). The arguments are also explicitly exhibited for the system with a quartic anisotropy having the Potts symmetry.
Quantum Field Theories and Bogoliubou Transformations. S. N. M. RUIJSENAARS.Department of Physics, Princeton University, Princeton, New Jersey 08544.
Integrable
The Federbush, massless Thirring and continuum lsing models and related integrable relativistic quantum field theories are studied. It is shown that local and covariant classical field operators exist that generate Bogoliubov transformations of the annihilation and creation operators on the Fock spaces of the respective models. The quantum fields of these models are closely related or equal to quadratic forms implementing these transformations, and hence formally inherit the covariance and locality of the underlying classical field operators. It is proved that the Federbush and massless Thirring fields on the physical sector do not satisfy the equation of motion. Closely related fields are defined that do satisfy it, and which lead to the same S-matrix, but these fields are presumably nonlocal. Bethe transforms are constructed for the various models, and on the unphysical sector the relation with the field theory approach is established.
Analysis in Field Theory. P. M. STEVENSON.Physics Department, University of WisconsinMadison, Madison, Wisconsin 53706.
Dimensional
Dimensional Transmutation (the breakdown of scale invariance in field theories) is reconciled with the commonsense notions of Dimensional Analysis. This makes possible a discussion of the meaning of the Renormalisation Group equations, completely divorced from the technicalities of renormalisation. As illustrations, I describe some very familiar QCD results in these terms.
The Gauge
Transformations
Physique Theorique,
of the Schwinger Model. A. K. RAINA AND Universite de Lausanne, Lausanne, Switzerland.
G. WANDERS. Institut de
We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model’s vacuum structure. 235 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.