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Phase space path integration of integrable quantum systems
ANNALS
OF PHYSICS
198, 201~202
Abstracts
(1990)
of Papers
to Appear
in Future
Issues
Topological Solitons and Temperature Effects in Gauge Field Theory. R. MANKA. Department of Theoretical Physics, Silesian University, Katowice 40007. Poland; AN‘;D G. VITIELLO. Dipartimento di Fisica dell’Universitl. 84100 Salerno, Italy. and lstituto Nazionale di Fisica Nucleare, Sezionc di Napoli, Napoli. Italy. We study temperature effects on homogeneous and nonhomogeneous boson condensation in gauge field theories in both abelian and nonabelian cases. Temperature-dependent vortex, monopole, and sphaleron equations are obtained. It is found that symmetry restoration can occur at the critical temperature at which the topological solitons vanish. The nonabelian character appears as temperature dependence of the magnetic charge.
W’igner’s Funcfion and Tunneling. N. sity of California, Santa Barbara.
L. BALAZS
A. VOROS. Institute 93106.
AND
California
for Theoretical
Physics,
Univer-
We construct Wigner’s functions of a system with the potential&ftu’q’ to exhibit and resolve some paradoxical features present in this description. Among others, we show that tunneling at negative energies arises through real trajectories associated with positive energies, in contradistinction of the usual WKB picture where this effect comes about by using complex trajectories of the correct energy. We resolve this puzzle by showing (a) that the initial data of this quanta1 description already contain “wrong” energy regions, and (b) that the interference phenomenon of WKB wave functions which provides the main contribution to Wigner’s function in the semiclassical domain becomes strongly nonlocul in the presence of a separatrix, which not only allows, but necessitates the presence of these “wrong” classical trajectories in the present description.
Phase
Space Path Integration ofIntegrable Qurtntum Systems. ARLEN ANDERSON. University of Utah, Salt Lake City, Utah, 84112: AND SCOTT B. ANDERSON. Montana State University, Bozeman. Montana 59717.
Department Department
of Physics, of Physics,
A new method for exact evaluation of phase space path integrals for integrable quantum systems is presented. By making use of point canonical and other transformations to bring the Hamiltonian to a form linear in the coordinates, the path integral is changed so that the functional 4 integration may be done. This produces a momentum delta functional which can be evaluated to give an ordinary integral. This procedure is applied to find an expression for the exact propagator for a particle in the harmonic oscillator potential, the inverse quadratic potential, the Coulomb potential, the Morse potential, and the I/cash’(x) potential, and for a free particle propagating on the ?-sphere. The latter two problems are solved for the first time wholly within the path integral formalism.
Classical Limit for Lie Algebras. AUREL Cyclotron Laboratory and Department Lansing, Michigan 48824-1321.
BULGAC
We present a general method to construct symplectic ‘-form. which defmes the Poisson
AND
of Physics
DIMITRI KUSNEZOV. National Superconducting and Astronomy, Michigan State University. East
the classical canonical coordinates structure is constructed explicitly.
for any Lie algebra. The In this way we are able
201 0003-49
l6/90
$7.50
CopyrIght ” 1990 by Academic Press, Inc All rights of reproduction III any form reserved
OF PHYSICS
198, 201~202
Abstracts
(1990)
of Papers
to Appear
in Future
Issues
Topological Solitons and Temperature Effects in Gauge Field Theory. R. MANKA. Department of Theoretical Physics, Silesian University, Katowice 40007. Poland; AN‘;D G. VITIELLO. Dipartimento di Fisica dell’Universitl. 84100 Salerno, Italy. and lstituto Nazionale di Fisica Nucleare, Sezionc di Napoli, Napoli. Italy. We study temperature effects on homogeneous and nonhomogeneous boson condensation in gauge field theories in both abelian and nonabelian cases. Temperature-dependent vortex, monopole, and sphaleron equations are obtained. It is found that symmetry restoration can occur at the critical temperature at which the topological solitons vanish. The nonabelian character appears as temperature dependence of the magnetic charge.
W’igner’s Funcfion and Tunneling. N. sity of California, Santa Barbara.
L. BALAZS
A. VOROS. Institute 93106.
AND
California
for Theoretical
Physics,
Univer-
We construct Wigner’s functions of a system with the potential&ftu’q’ to exhibit and resolve some paradoxical features present in this description. Among others, we show that tunneling at negative energies arises through real trajectories associated with positive energies, in contradistinction of the usual WKB picture where this effect comes about by using complex trajectories of the correct energy. We resolve this puzzle by showing (a) that the initial data of this quanta1 description already contain “wrong” energy regions, and (b) that the interference phenomenon of WKB wave functions which provides the main contribution to Wigner’s function in the semiclassical domain becomes strongly nonlocul in the presence of a separatrix, which not only allows, but necessitates the presence of these “wrong” classical trajectories in the present description.
Phase
Space Path Integration ofIntegrable Qurtntum Systems. ARLEN ANDERSON. University of Utah, Salt Lake City, Utah, 84112: AND SCOTT B. ANDERSON. Montana State University, Bozeman. Montana 59717.
Department Department
of Physics, of Physics,
A new method for exact evaluation of phase space path integrals for integrable quantum systems is presented. By making use of point canonical and other transformations to bring the Hamiltonian to a form linear in the coordinates, the path integral is changed so that the functional 4 integration may be done. This produces a momentum delta functional which can be evaluated to give an ordinary integral. This procedure is applied to find an expression for the exact propagator for a particle in the harmonic oscillator potential, the inverse quadratic potential, the Coulomb potential, the Morse potential, and the I/cash’(x) potential, and for a free particle propagating on the ?-sphere. The latter two problems are solved for the first time wholly within the path integral formalism.
Classical Limit for Lie Algebras. AUREL Cyclotron Laboratory and Department Lansing, Michigan 48824-1321.
BULGAC
We present a general method to construct symplectic ‘-form. which defmes the Poisson
AND
of Physics
DIMITRI KUSNEZOV. National Superconducting and Astronomy, Michigan State University. East
the classical canonical coordinates structure is constructed explicitly.
for any Lie algebra. The In this way we are able
201 0003-49
l6/90
$7.50
CopyrIght ” 1990 by Academic Press, Inc All rights of reproduction III any form reserved