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On quantum mechanics with extended supersymmetry and nonabelian gauge constraints
ANNALS OF PHYSICS 163, 473474
Abstracts
(1985)
of Papers
to Appear
in Future
Issues
On Quantum Mechanics with E,xtended Supersymmetry and Nonabelian Gauge Constraints. R. Physikalisches Institut der Universitlt Bonn, Nussallee 12, 5300 Bonn 1, West Germany.
FLUME,
A weakly restricted general class of quantum mechanical models with at least four real supercharges and nonabelian gauge constraints is analyzed. The innocently looking restrictions lead automatically and exclusively to the quantum mechanics which are the dimensionally reduced counterparts of supersymmetric Yang-Mills field theories. This result provides in turn an independent proof that N = 1, N = 2, and N =4 Yang-Mills fields are the only possible supersymmetric gauge field theories (without central charges) in four dimensions.
Group
Manifold Analysis of the Structure of Relativistic Quantum Dynamics. ViCTOR ALDAYA AND Jo& A. DE AZCARRAGA, Departamento de Fisica Teorica, Facultad de Ciencias Fisicas, Universidad de Valencia, Burjasot (Valencia), Spain.
Presented here is a group law, derived as a contraction of the conformal group, from which a relativistic quantum system with an invariant evolution parameter (the proper time) is obtained by using a canonical procedure and where the position operator belongs to the Lie algebra of the group. The restriction of the theory to the mass shell breaks part of the symmetry: of the previous 15 generators, only 10 remain which generate an action of the Poincare group defining an orbit in the former group manifold. Some comments on the relativistic position operator are also made.
On the Connection between D.vons, Vortices, and Aharonov-Bohm @firI. A. 0. BARUT, Department Physics, University of Colorado, Boulder, Colorado 80309, AND RAJ WILSON, Department Mathematics, University of Georgia, Athens, Georgia 30602.
of of
A unitied group theoretical exact solution is given for the motion of a charge in the field of a monopole (with Dirac or Schwinger strings), a solenoid, and monopoles with spin (or isospin) quantum numbers, or their linear combinations. For all these cases the dynamical group is SO(4, 2) and the treatment illuminates in a most general way the recent discussion about the quantum numbers and charge and flux quantizations. Even if the flux in the solenoid is not quantized the problem can be solved in terms of the unitary supplementary series of representations of the Lorentz subgroup.
Representations of Spacetime Diffeomorphisms. I. Canonical Parametrized Field Theories. C. J. ISHAM AND K. V. KUCHAR, The Blackett Laboratory. Imperial College, Prince Consort Road, London SW7 2BZ, United Kingdom. The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametrized field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields BE L Diff Z on the space manifold Z, the Lie algebra L Diff C of the spatial diffeomorphism group Diff ,!I can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the
473 X103-4916/85 Copyright All
rights
8 of
1985
reproduction
by
Academic in any
$7.50 Press.
form
reserved.
Inc.
Abstracts
(1985)
of Papers
to Appear
in Future
Issues
On Quantum Mechanics with E,xtended Supersymmetry and Nonabelian Gauge Constraints. R. Physikalisches Institut der Universitlt Bonn, Nussallee 12, 5300 Bonn 1, West Germany.
FLUME,
A weakly restricted general class of quantum mechanical models with at least four real supercharges and nonabelian gauge constraints is analyzed. The innocently looking restrictions lead automatically and exclusively to the quantum mechanics which are the dimensionally reduced counterparts of supersymmetric Yang-Mills field theories. This result provides in turn an independent proof that N = 1, N = 2, and N =4 Yang-Mills fields are the only possible supersymmetric gauge field theories (without central charges) in four dimensions.
Group
Manifold Analysis of the Structure of Relativistic Quantum Dynamics. ViCTOR ALDAYA AND Jo& A. DE AZCARRAGA, Departamento de Fisica Teorica, Facultad de Ciencias Fisicas, Universidad de Valencia, Burjasot (Valencia), Spain.
Presented here is a group law, derived as a contraction of the conformal group, from which a relativistic quantum system with an invariant evolution parameter (the proper time) is obtained by using a canonical procedure and where the position operator belongs to the Lie algebra of the group. The restriction of the theory to the mass shell breaks part of the symmetry: of the previous 15 generators, only 10 remain which generate an action of the Poincare group defining an orbit in the former group manifold. Some comments on the relativistic position operator are also made.
On the Connection between D.vons, Vortices, and Aharonov-Bohm @firI. A. 0. BARUT, Department Physics, University of Colorado, Boulder, Colorado 80309, AND RAJ WILSON, Department Mathematics, University of Georgia, Athens, Georgia 30602.
of of
A unitied group theoretical exact solution is given for the motion of a charge in the field of a monopole (with Dirac or Schwinger strings), a solenoid, and monopoles with spin (or isospin) quantum numbers, or their linear combinations. For all these cases the dynamical group is SO(4, 2) and the treatment illuminates in a most general way the recent discussion about the quantum numbers and charge and flux quantizations. Even if the flux in the solenoid is not quantized the problem can be solved in terms of the unitary supplementary series of representations of the Lorentz subgroup.
Representations of Spacetime Diffeomorphisms. I. Canonical Parametrized Field Theories. C. J. ISHAM AND K. V. KUCHAR, The Blackett Laboratory. Imperial College, Prince Consort Road, London SW7 2BZ, United Kingdom. The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametrized field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields BE L Diff Z on the space manifold Z, the Lie algebra L Diff C of the spatial diffeomorphism group Diff ,!I can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the
473 X103-4916/85 Copyright All
rights
8 of
1985
reproduction
by
Academic in any
$7.50 Press.
form
reserved.
Inc.