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Chiral symmetry breakdown, anomaly and the PCAC relation on a lattice
ANNALS
OF PHYSICS
152, 236-237
Abstracts
(1984)
of Papers to Appear in Future Issues
Field Theoretical Treatment of Approximations FULTON. Department of Physics, The Johns
to Radiative Transitions in Atoms. G. FELDMAN AND T. Hopkins University, Baltimore, Maryland 21218.
Starting with a field theoretical many-body definition of eigenvalues and radiative transition matrix elements for atomic systems, a systematic approach is taken to approximations of the exact results. The guiding principle is the maintenance of gauge invariance (GI) in radiative transition S matrix elements. At the level of the one Coulomb exchange approximation in both the one electron and the electron-hole propagator kernels, one obtains the well known Hartree-Fock (HF) and random phase approximations (RPA). A detailed discussion and comparison of various approaches to RPA is made, in the case of both N and N - 1 electron shielding (the regular HF and HF with frozen relaxed core-FRC). In the former case, a new and considerably simpler form of the RPA equations is obtained than heretofore proposed equivalent forms. Finally, an approximation different from the usual HF and RPA, involving higher order correlations. is developed to illustrate how such approximations can be systematicaily generated.
Chiral Symmetry Breakdown, Anomaly Department of Physics, Tokyo Institute
and the PCAC Relation of Technology, Oh-okayama,
on
a Lattice. Meguro-ku,
IKUO
Tokyo
ICHINOSE.
152, Japan.
Lattice fermion formulation is investigated using a solvable model which resembles Quantum Chromodynamics. CPY- ’ models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the l/N expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) mass is calculated. From the above results, it is shown apparently occurs in this model, and the “pion” that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.
Time-Independent THOMPSON.
Mean Daresbury
Field Description of Collisions. Laboratory. Warrington WA4
B. G. GIRAUD, 4AD, U.K.
M.
A. NAGARAJAN,
AND I. J.
Products of single-particle orbitals are used as trial functions in a variational principle for the calculation of multistep nuclear collisions. The resulting dynamical equations are time-independent and generalize Hartree equations to nondiagonal mean fields with inhomogeneous source terms. These equations are solved for a p + 3H +p + n + d breakup reaction.
Renormalized Storage
Fokker-Plank Equation for the Problem of the Beam-Beam Rings. F. RUGGIERO. Scuola Normale Superiore, Pisa, Italy.
Interaction
in Electron
It is shown that the beam-beam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron oscillations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the
236 0003.4916184
$7.50
Copyright C 1984 by Academic Press. Inc. All rights of reproduction in any form reserved.
OF PHYSICS
152, 236-237
Abstracts
(1984)
of Papers to Appear in Future Issues
Field Theoretical Treatment of Approximations FULTON. Department of Physics, The Johns
to Radiative Transitions in Atoms. G. FELDMAN AND T. Hopkins University, Baltimore, Maryland 21218.
Starting with a field theoretical many-body definition of eigenvalues and radiative transition matrix elements for atomic systems, a systematic approach is taken to approximations of the exact results. The guiding principle is the maintenance of gauge invariance (GI) in radiative transition S matrix elements. At the level of the one Coulomb exchange approximation in both the one electron and the electron-hole propagator kernels, one obtains the well known Hartree-Fock (HF) and random phase approximations (RPA). A detailed discussion and comparison of various approaches to RPA is made, in the case of both N and N - 1 electron shielding (the regular HF and HF with frozen relaxed core-FRC). In the former case, a new and considerably simpler form of the RPA equations is obtained than heretofore proposed equivalent forms. Finally, an approximation different from the usual HF and RPA, involving higher order correlations. is developed to illustrate how such approximations can be systematicaily generated.
Chiral Symmetry Breakdown, Anomaly Department of Physics, Tokyo Institute
and the PCAC Relation of Technology, Oh-okayama,
on
a Lattice. Meguro-ku,
IKUO
Tokyo
ICHINOSE.
152, Japan.
Lattice fermion formulation is investigated using a solvable model which resembles Quantum Chromodynamics. CPY- ’ models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the l/N expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) mass is calculated. From the above results, it is shown apparently occurs in this model, and the “pion” that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.
Time-Independent THOMPSON.
Mean Daresbury
Field Description of Collisions. Laboratory. Warrington WA4
B. G. GIRAUD, 4AD, U.K.
M.
A. NAGARAJAN,
AND I. J.
Products of single-particle orbitals are used as trial functions in a variational principle for the calculation of multistep nuclear collisions. The resulting dynamical equations are time-independent and generalize Hartree equations to nondiagonal mean fields with inhomogeneous source terms. These equations are solved for a p + 3H +p + n + d breakup reaction.
Renormalized Storage
Fokker-Plank Equation for the Problem of the Beam-Beam Rings. F. RUGGIERO. Scuola Normale Superiore, Pisa, Italy.
Interaction
in Electron
It is shown that the beam-beam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron oscillations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the
236 0003.4916184
$7.50
Copyright C 1984 by Academic Press. Inc. All rights of reproduction in any form reserved.