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On bogoliubov transformations. II. The general case
ANNALS OF PHYSICS
115,
496-497
Abstracts
(1978)
of Papers
to Appear
in Future
Issues
of, and the y-Radiation from, the p-Shell Hypernuclei. R. H. DALITZ. Department of Theoretical Physics, Oxford University, Oxford, England; AND A. GAL, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel.
The Formation
The physical factors relevant for the production of various low-lying A-hypernuclear states jZ* through the K-- + p- and Km + pLoreactions, in flight or from rest, on the corresponding target nuclei ‘Z and A(Z + 1) are discussed, on the basis of the shell model for these nuclei and hypernuclei, together with the characteristics of the dominant y-transitions resulting from the excited states thus produced. Detailed consideration is given for a number of hypernuclei of specific interest, including the cases of JHe, ALi for A = 7,9 and 10, ,tBe for A = 9 and 10, LB for A = 10, II, and 12, AC for A = 12. 13, 14, and 15,4N for A = 14 and 15, and 20. The importance of (y, p-) correlation studies for the determination of hypernuclear spin values is stressed, with the discussion of several examples. Hamiltonian
Formulation
of the
Theory
of Interacting
AND C. TEITELBOIM. Joseph Henry Laboratories,
Gravitational
Princeton
and Electron Fields. J. E. NELSON University, Princeton, New Jersey
08540.
The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x0 = constant hypersurfaces (“time gauge”) the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent. Extended Electron Model. P. GNADIG AND Z. KUNSZT. Department of Atomic Physics, Roland Eotviis University, 1088 Budapest, Puskin u. 5-7, Hungary; AND P. HASENFRATZ AND J. KUTI. Central Research Institute for Physics, Hungarian Academy of Sciences, 1525 Budapest 114, POB. 49, Hungary.
Dirac’s
Dirac’s extended electron model is elaborated here both on the classical and quantum level. The classical equations of motion are deduced from Dirac’s action principle. It is shown that the model is free of the troublesome runaway solutions already in the classical theory. The quantum theory of the radial oscillations is worked out in detail and the spectrum is discussed. The stability of the model is studied and it is found that Dirac’s extended electron is unstable against quadrupole deformations. On Bogoliubov
transformations.
II.
The general
case. S.
N. M. RUIJSENAARS.Department of Physics,
Princeton University, Princeton, New Jersey 08540. A rigorous treatment of Bogoliubov transformations is presented along the same lines as in a previous paper (I), which dealt with a special case. As in (1) a formulation in terms of unitary resp. pseudo-unitary operators is used, corresponding to the CAR resp. the CCR. This leads to simple proofs of well-known necessary and sufficient conditions for the transformation to be unitarily implementable in Fock space. The normal form of the implementing operator % is studied. It is
496 OCQ3-4916/78/1152Xl496$05.00/0 Copyright All rights
0 1978 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
497
proved that on the subspace of algebraic tensors Q equals a strongly convergent infinite series of Wick monomials that sums up to a simple exponential expression. A connection between the fermion and boson transformations studied in (1) is established. The analogous correspondence in the general case only holds true if the (pseudo) unitary operator equals its own inverse.
115,
496-497
Abstracts
(1978)
of Papers
to Appear
in Future
Issues
of, and the y-Radiation from, the p-Shell Hypernuclei. R. H. DALITZ. Department of Theoretical Physics, Oxford University, Oxford, England; AND A. GAL, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel.
The Formation
The physical factors relevant for the production of various low-lying A-hypernuclear states jZ* through the K-- + p- and Km + pLoreactions, in flight or from rest, on the corresponding target nuclei ‘Z and A(Z + 1) are discussed, on the basis of the shell model for these nuclei and hypernuclei, together with the characteristics of the dominant y-transitions resulting from the excited states thus produced. Detailed consideration is given for a number of hypernuclei of specific interest, including the cases of JHe, ALi for A = 7,9 and 10, ,tBe for A = 9 and 10, LB for A = 10, II, and 12, AC for A = 12. 13, 14, and 15,4N for A = 14 and 15, and 20. The importance of (y, p-) correlation studies for the determination of hypernuclear spin values is stressed, with the discussion of several examples. Hamiltonian
Formulation
of the
Theory
of Interacting
AND C. TEITELBOIM. Joseph Henry Laboratories,
Gravitational
Princeton
and Electron Fields. J. E. NELSON University, Princeton, New Jersey
08540.
The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x0 = constant hypersurfaces (“time gauge”) the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent. Extended Electron Model. P. GNADIG AND Z. KUNSZT. Department of Atomic Physics, Roland Eotviis University, 1088 Budapest, Puskin u. 5-7, Hungary; AND P. HASENFRATZ AND J. KUTI. Central Research Institute for Physics, Hungarian Academy of Sciences, 1525 Budapest 114, POB. 49, Hungary.
Dirac’s
Dirac’s extended electron model is elaborated here both on the classical and quantum level. The classical equations of motion are deduced from Dirac’s action principle. It is shown that the model is free of the troublesome runaway solutions already in the classical theory. The quantum theory of the radial oscillations is worked out in detail and the spectrum is discussed. The stability of the model is studied and it is found that Dirac’s extended electron is unstable against quadrupole deformations. On Bogoliubov
transformations.
II.
The general
case. S.
N. M. RUIJSENAARS.Department of Physics,
Princeton University, Princeton, New Jersey 08540. A rigorous treatment of Bogoliubov transformations is presented along the same lines as in a previous paper (I), which dealt with a special case. As in (1) a formulation in terms of unitary resp. pseudo-unitary operators is used, corresponding to the CAR resp. the CCR. This leads to simple proofs of well-known necessary and sufficient conditions for the transformation to be unitarily implementable in Fock space. The normal form of the implementing operator % is studied. It is
496 OCQ3-4916/78/1152Xl496$05.00/0 Copyright All rights
0 1978 by Academic Press, Inc. of reproduction in any form reserved.
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
497
proved that on the subspace of algebraic tensors Q equals a strongly convergent infinite series of Wick monomials that sums up to a simple exponential expression. A connection between the fermion and boson transformations studied in (1) is established. The analogous correspondence in the general case only holds true if the (pseudo) unitary operator equals its own inverse.