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Electron radiative self-energy of highly stripped heavy atoms
ANNALS
OF PHYSICS 210,
48&487
Abstracts
Natural
Scales
for
(1991)
of Papers
Interacting
Fields
to Appear
Defined
on a Set of Discrete
in Future
Points.
Issues
M. C. BERG~RE.Service de
Physique Theorique de Saclay, F-91191 Gif-sur-Yvette, Cedex, France. We generalize the definition of natural scales (originally defined on a single point) to systems of interacting fields defined on a set of discrete, correlated points. We study the case of a nearest neighbour interaction over a d-dimensional rectangular lattice; the thermodynamic limit of natural scales is defined.
Integrals for Abelian Anomalous Gauge Theories. P. MITRA. Theoretical Nuclear Physics Division, Saha Institute of Nuclear Physics, Block AF, Bidhannagar, Calcutta-700 064, India.
Functional
The functional integral for a four-dimensional abelian anomalous gauge theory is constructed by taking constraints and anomalies into account. It is found to differ from the naive Lagrangian form. A gauge invariant reformulation is possible, provided (gauge-) covariant anomalies are used. In both formulations, Lorentz invariance seems to be violated. The two-dimensional chiral Schwinger model, if treated in the same way, leads to the familiar gauge invariant formulation which is Lorentz invariant.
Electron
Radiative
Self-Energy
of Highly
Stripped
Heavy
California, Lawrence Livermore National Laboratory,
NEAL J. SNYDERMAN.University of Livermore, California 94550.
Atoms.
A new algorithm is presented for the evaluation of the electron radiative self-energy in heavy atoms, for which Za is not a perturbative expansion parameter. The algorithm for hydrogenic ions is presented in detail. The terms to be evaluated numerically are finite, free of spurious gauge dependent parts, and are not in the form of a subtraction. The extension to many electron ions is also discussed.
A Semiclassical
Theory
of Quasienergies
and Floquet
Wave Functions.
H. P. BREUER AND M.
HOLTHAUS.
Physikalisches Institut der Universitat Bonn, Nussallee 12, D-5300 Bonn 1, Germany. Employing the Maslov construction of the canonical operator, we derive semiclassical quantization rules for quasienergies and Floquet states of periodically time-dependent systems. The method is applied to a class of strongly driven anharmonic oscillators which, on the classical level, show a sharp division of the phase space into an almost regular and a stochastic region. For the almost regular part of motion the semiclassical quantization rules are shown to yield excellent approximations to the exact quantum mechanical quasienergies and Floquet states. The influence of resonances and stochastic motion on quasienergy spectra and Floquet wave functions is discussed. We demonstrate that an exact scaling relation valid for the classical Hamiltonian leads to an approximate scaling relation for the quasienergies which is broken in a characteristic manner by quantum effects.
486 0003-4916/91 $7.50 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
OF PHYSICS 210,
48&487
Abstracts
Natural
Scales
for
(1991)
of Papers
Interacting
Fields
to Appear
Defined
on a Set of Discrete
in Future
Points.
Issues
M. C. BERG~RE.Service de
Physique Theorique de Saclay, F-91191 Gif-sur-Yvette, Cedex, France. We generalize the definition of natural scales (originally defined on a single point) to systems of interacting fields defined on a set of discrete, correlated points. We study the case of a nearest neighbour interaction over a d-dimensional rectangular lattice; the thermodynamic limit of natural scales is defined.
Integrals for Abelian Anomalous Gauge Theories. P. MITRA. Theoretical Nuclear Physics Division, Saha Institute of Nuclear Physics, Block AF, Bidhannagar, Calcutta-700 064, India.
Functional
The functional integral for a four-dimensional abelian anomalous gauge theory is constructed by taking constraints and anomalies into account. It is found to differ from the naive Lagrangian form. A gauge invariant reformulation is possible, provided (gauge-) covariant anomalies are used. In both formulations, Lorentz invariance seems to be violated. The two-dimensional chiral Schwinger model, if treated in the same way, leads to the familiar gauge invariant formulation which is Lorentz invariant.
Electron
Radiative
Self-Energy
of Highly
Stripped
Heavy
California, Lawrence Livermore National Laboratory,
NEAL J. SNYDERMAN.University of Livermore, California 94550.
Atoms.
A new algorithm is presented for the evaluation of the electron radiative self-energy in heavy atoms, for which Za is not a perturbative expansion parameter. The algorithm for hydrogenic ions is presented in detail. The terms to be evaluated numerically are finite, free of spurious gauge dependent parts, and are not in the form of a subtraction. The extension to many electron ions is also discussed.
A Semiclassical
Theory
of Quasienergies
and Floquet
Wave Functions.
H. P. BREUER AND M.
HOLTHAUS.
Physikalisches Institut der Universitat Bonn, Nussallee 12, D-5300 Bonn 1, Germany. Employing the Maslov construction of the canonical operator, we derive semiclassical quantization rules for quasienergies and Floquet states of periodically time-dependent systems. The method is applied to a class of strongly driven anharmonic oscillators which, on the classical level, show a sharp division of the phase space into an almost regular and a stochastic region. For the almost regular part of motion the semiclassical quantization rules are shown to yield excellent approximations to the exact quantum mechanical quasienergies and Floquet states. The influence of resonances and stochastic motion on quasienergy spectra and Floquet wave functions is discussed. We demonstrate that an exact scaling relation valid for the classical Hamiltonian leads to an approximate scaling relation for the quasienergies which is broken in a characteristic manner by quantum effects.
486 0003-4916/91 $7.50 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.