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The potential harmonic expansion method
ANNALS
OF PHYSICS
147, 267-268
Abstracts
The Potential Harmonic Institut de Physique
(1983)
of Papers to Appear
Expansion Nucliaire.
Method. F-91406
in Future
M. FABRE DE LA RIPELLE. Orsay Cedex, France.
Division
Issues
de Physique
Thtorique.
Various properties of the hyperspherical potential basis are investigated. The expansion of any twobody function, in particular the two-body potential, is given. The matrix elements with two and three potential harmonics needed for the construction of the potential matrix are calculated. Useful recurrence formulae arc derived. The concept of potential basis is extended to systems with any number of fermions. A method for improving the accuracy of the expansion of the wavefunction by taking into account more than the two-body correlations is suggested.
Functional Integral Mean Field Expansions for Nuclear Many Fermion Systems. A. K. KERMAN. S. LEVIT. AND T. TROUDET. Center for Theoretical Physics. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology. Cambridge, Massachusetts 02 139. A careful analysis of the auxiliary field functional integral formalism for many fermion systems is presented. The limiting procedure used in construction of such integrals is examined and it is shown that a wide flexibility exists with respect to the choice of the one body field representation upon which mean field expansions are made. The utility of this flexibility in the context of the evaluation of the grand canonical partition function is demonstrated. The zero order. RPA. and certain higher order terms are examined. The above mentioned flexibility is reflected in the dependence of the results on a trial two body interaction. different choices of which produce Hartree. Fock. Hartree-Fock. or other forms of the mean field expansions. A standard variational procedure selects the Hartree-Fock as the optimal choice. With this choice certain corrections to previously reported RPA contributions for the Hartree mean field are found. Also indicated is the relevance of the authors’ formulation for the recent applications of the functional integral mean field approach to nuclear dynamical problems.
A S.wtematic Technical Theoretical
Search for a Realistic SU(N) Tumbling Gauge Model. GBN~~L SCALP. IJniversity. Physics Department, Ankara, Turkey; AND SINAN KAPTANOGLU. Physics. State University of New York, Stony Brook, New York 11794.
Middle East Institute for
Within the framework of the dynamical symmetry breaking and the Tumbling ideas, a systematic search was carried out in SC/(n) groups with the ultimate aim of determining if a realistic and phenomenologically acceptable model exists which tumbles down to SU(3) @ U(I ), or a suitable larger group. To do so all the anomaly free and the asymptotically free fermion contents for any SC/(n) were first determined. In order to have nontrivial Tumbling the real and the pseudo-real representations have been eliminated. and the Tumbling patterns of all the allowed complex ones have been examined in detail. No such realistic model has been found. These results combined with that of Srednicki’s concerning the SO(4n + 2) and E, groups establish the fact that there cannot be any realistic Tumbling gauge model within the context of the original Tumbling hypotheses. Having thus established the need for a change of these hypotheses we make some suggestions and comment on various ways of remedying the problem.
267 0003.4916183
$7.50
Copyright C 1983 by Academic Press, Inc. All rights of reproduction in any form reserved.
OF PHYSICS
147, 267-268
Abstracts
The Potential Harmonic Institut de Physique
(1983)
of Papers to Appear
Expansion Nucliaire.
Method. F-91406
in Future
M. FABRE DE LA RIPELLE. Orsay Cedex, France.
Division
Issues
de Physique
Thtorique.
Various properties of the hyperspherical potential basis are investigated. The expansion of any twobody function, in particular the two-body potential, is given. The matrix elements with two and three potential harmonics needed for the construction of the potential matrix are calculated. Useful recurrence formulae arc derived. The concept of potential basis is extended to systems with any number of fermions. A method for improving the accuracy of the expansion of the wavefunction by taking into account more than the two-body correlations is suggested.
Functional Integral Mean Field Expansions for Nuclear Many Fermion Systems. A. K. KERMAN. S. LEVIT. AND T. TROUDET. Center for Theoretical Physics. Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology. Cambridge, Massachusetts 02 139. A careful analysis of the auxiliary field functional integral formalism for many fermion systems is presented. The limiting procedure used in construction of such integrals is examined and it is shown that a wide flexibility exists with respect to the choice of the one body field representation upon which mean field expansions are made. The utility of this flexibility in the context of the evaluation of the grand canonical partition function is demonstrated. The zero order. RPA. and certain higher order terms are examined. The above mentioned flexibility is reflected in the dependence of the results on a trial two body interaction. different choices of which produce Hartree. Fock. Hartree-Fock. or other forms of the mean field expansions. A standard variational procedure selects the Hartree-Fock as the optimal choice. With this choice certain corrections to previously reported RPA contributions for the Hartree mean field are found. Also indicated is the relevance of the authors’ formulation for the recent applications of the functional integral mean field approach to nuclear dynamical problems.
A S.wtematic Technical Theoretical
Search for a Realistic SU(N) Tumbling Gauge Model. GBN~~L SCALP. IJniversity. Physics Department, Ankara, Turkey; AND SINAN KAPTANOGLU. Physics. State University of New York, Stony Brook, New York 11794.
Middle East Institute for
Within the framework of the dynamical symmetry breaking and the Tumbling ideas, a systematic search was carried out in SC/(n) groups with the ultimate aim of determining if a realistic and phenomenologically acceptable model exists which tumbles down to SU(3) @ U(I ), or a suitable larger group. To do so all the anomaly free and the asymptotically free fermion contents for any SC/(n) were first determined. In order to have nontrivial Tumbling the real and the pseudo-real representations have been eliminated. and the Tumbling patterns of all the allowed complex ones have been examined in detail. No such realistic model has been found. These results combined with that of Srednicki’s concerning the SO(4n + 2) and E, groups establish the fact that there cannot be any realistic Tumbling gauge model within the context of the original Tumbling hypotheses. Having thus established the need for a change of these hypotheses we make some suggestions and comment on various ways of remedying the problem.
267 0003.4916183
$7.50
Copyright C 1983 by Academic Press, Inc. All rights of reproduction in any form reserved.