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Linear response of hot gluons
ANNALS
OF PHYSICS
189, 461462 (1989)
Abstracts
Linear
of Papers
to Appear
in Future
Issues
Response 01 Hot Gluons. M. E. CARRINGTON, T. H. HANSON, H. YAMAGISHI, AND I. ZAHED. Physics Department, State University of New York, Stony Brook, New York 11794.
We reexamine the various schemes for calculating the linear response (the retarded Green’s function) of a hot gluon plasma. The problems related to gauge invariance are discussed in detail, and results in different gauges are compared. We also point out some issues related to the very definition of a thermal ensemble in the presence of unphysical degrees of freedom. By calculating the retarded Green’s function directly in real time, we explicitly study the effects of unphysical degrees of freedom in different gauges. Although there appears to be no unique way to deline the response function, we find that several schemes can be questioned on formal grounds and that use of the background-field gauge (BFG) is the most satisfactory in this respect. We discuss two proposals to fix the gauge parameter (a) dependence in the BFG response function, the Vilkovisky-Dewitt effective action corresponding to the choice a = 0 (background Landau gauge), and the “gauge-invariant propagator” of Cornwall et al. corresponding to a = 1 (background Feynman gauge).
Spinodal
Decomposition
in Quantum
Field Theory.
ESTEBAN
CALZETTA.
Ins!itute for Theoretical Physics,
University of Alberta, Edmonton, Alberta, Canada T6G 251. We investigate the dynamics of spinodal decomposition in quantum field theory. We consider a Q4 scalar field with tachyonic mass n2 < 0 which is suddenly brought into contact with a heat bath at zero temperature. By using the two-particle irreducible closed-time-path effective action we give a detailed description of how fluctuations in the infrared end of the spectrum grow to give rise to a Bose-Einstein condensate. The later time behavior of the phase decomposition is described by mean field theory.
Baker’s Transformation. N. L. BALAZS. Department of Physics, State University of New York, Stony Brook, New York 11794; AND A. VOROS.Service de Physique Theorique, Institut de Recherche Fondamentale, CEA-CEN Saclay, 91191 Gif-sur-Yvette Cedex, France.
The Quantized
A quantum analogue of the Baker’s transformation is constructed using a specially developed quantization procedure. We obtain a unitary operator acting on an N-dimensional Hilbert space, with N finite (and even), that has properties similar to those of the classical baker’s map and reduces to it in the classical limit, which corresponds here to N -+ 0~).The operator can be described as a very simple, fully explicit N x N matrix. Numerical investigations confirm that this model has non-trivial features which ought to represent quanta1 manifestations of classical chaoticity. The quasi-energy spectrum is given by irrational eigenangles, leading to no recurrences. Most eigenfunctions look irregular, but some exhibit puzzling regular features, such as peaks at coordinate values belonging to periodic orbits of the classical baker’s map. We compare the quanta1 and classical time-evolutions, as applied to initially coherent quasi-classical states: the evolving states stay in close agreement for short times but seem to lose all relationship to each other beyond a critical time of the order of log, N m -log fi.
461 0003-4916/89 $7.50 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form rcscrved.
OF PHYSICS
189, 461462 (1989)
Abstracts
Linear
of Papers
to Appear
in Future
Issues
Response 01 Hot Gluons. M. E. CARRINGTON, T. H. HANSON, H. YAMAGISHI, AND I. ZAHED. Physics Department, State University of New York, Stony Brook, New York 11794.
We reexamine the various schemes for calculating the linear response (the retarded Green’s function) of a hot gluon plasma. The problems related to gauge invariance are discussed in detail, and results in different gauges are compared. We also point out some issues related to the very definition of a thermal ensemble in the presence of unphysical degrees of freedom. By calculating the retarded Green’s function directly in real time, we explicitly study the effects of unphysical degrees of freedom in different gauges. Although there appears to be no unique way to deline the response function, we find that several schemes can be questioned on formal grounds and that use of the background-field gauge (BFG) is the most satisfactory in this respect. We discuss two proposals to fix the gauge parameter (a) dependence in the BFG response function, the Vilkovisky-Dewitt effective action corresponding to the choice a = 0 (background Landau gauge), and the “gauge-invariant propagator” of Cornwall et al. corresponding to a = 1 (background Feynman gauge).
Spinodal
Decomposition
in Quantum
Field Theory.
ESTEBAN
CALZETTA.
Ins!itute for Theoretical Physics,
University of Alberta, Edmonton, Alberta, Canada T6G 251. We investigate the dynamics of spinodal decomposition in quantum field theory. We consider a Q4 scalar field with tachyonic mass n2 < 0 which is suddenly brought into contact with a heat bath at zero temperature. By using the two-particle irreducible closed-time-path effective action we give a detailed description of how fluctuations in the infrared end of the spectrum grow to give rise to a Bose-Einstein condensate. The later time behavior of the phase decomposition is described by mean field theory.
Baker’s Transformation. N. L. BALAZS. Department of Physics, State University of New York, Stony Brook, New York 11794; AND A. VOROS.Service de Physique Theorique, Institut de Recherche Fondamentale, CEA-CEN Saclay, 91191 Gif-sur-Yvette Cedex, France.
The Quantized
A quantum analogue of the Baker’s transformation is constructed using a specially developed quantization procedure. We obtain a unitary operator acting on an N-dimensional Hilbert space, with N finite (and even), that has properties similar to those of the classical baker’s map and reduces to it in the classical limit, which corresponds here to N -+ 0~).The operator can be described as a very simple, fully explicit N x N matrix. Numerical investigations confirm that this model has non-trivial features which ought to represent quanta1 manifestations of classical chaoticity. The quasi-energy spectrum is given by irrational eigenangles, leading to no recurrences. Most eigenfunctions look irregular, but some exhibit puzzling regular features, such as peaks at coordinate values belonging to periodic orbits of the classical baker’s map. We compare the quanta1 and classical time-evolutions, as applied to initially coherent quasi-classical states: the evolving states stay in close agreement for short times but seem to lose all relationship to each other beyond a critical time of the order of log, N m -log fi.
461 0003-4916/89 $7.50 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form rcscrved.