Holonomy and the Einstein equations

Holonomy and the Einstein equations

474 ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES meson theory of interacting pions, p- and w-mesons. The nucleon properties are determined by ...

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474

ABSTRACTS

OF PAPERS

TO APPEAR

IN FUTURE

ISSUES

meson theory of interacting pions, p- and w-mesons. The nucleon properties are determined by the mesonic parameters. For the temperature dependence of these meson parameters, we use rigorous results from chiral perturbation theory as well as predictions from the Nambu-Jona-Lasinio model. We discuss bulk properties of the nucleon, electroweak form factors, strong and weak interaction regions. We stress the importance of these effects for the study of hadronic systems close to the chiral restoration phase transition. Furthermore, we derive an expression for the temperature dependence of the non-perturbative gluon condensate.

Holonomy and the Einstein National de Cordoba, Pittsburgh, Pittsburgh,

Equations. CARLOS KOZAMEH AND WALTER LAMBERTI. FaMAF, Argentina; AND EZRA T. NEWMAN. Department of Physics, Pennsylvania 15260.

Universidad University of

A new point of view towards the vacuum Einstein equations on asymptotically flat space-times is presented. This new perspective involves the introduction of two different non-local geometric objects as the basic variables-rather than the usual (local) metric and connection-and then to lind equations, equivalent to the Einstein field equations, satisfied by these variables. The first of these objects is the holonomy operator, i.e., the parallel propagator around closed curves, associated with a subclass of loops that arises naturally on asymptotically simple space-times. We establish the relationship between the holonomy operator and both the curvature tensor and connection of the space. The second non-local variable is the “light-cone cut function,” which analytically describes the intersection of the light cone from an arbitrary space-time point x”, with null infinity, the conformal boundary of the space-time. The field equations for the holonomy operator and the cut function are derived and several implications of this formalism are discussed.

Non-symmetric Double Well and Euclidean Functional Integral. FILIP~~ CESI. Courant Institute of matical Sciences, 251 Mercer Street, New York, New York 10012 and I.N.F.N., Sezione di Roma, Italy; GIAN CARLO ROSSI. Dipartimento di Fisica, Universita dell’Aquila, L’Aquila, and I.N.F.N., Laboratori Nazionali del Gran Sasso, L’Aquila, Italy; AND MASSIMO Dipartimento di Fisica, Universita di Lecce, Lecce, Italy and I.N.F.N., Sezione di Lecce, Italy.

MatheRoma, Italy TESTA. Lecce.

In this paper we show how it is possible to discuss in the language of functional integrals the problem of the symmetric double well with a small perturbation, in the semiclassical limit. This problem has been previously treated by means of a completely different approach, based on the theory of small random perturbations of dynamical systems. We recover all known resufis concerning the wave function and the energy splitting of the two lowest lying states, and we give an explicit expression for the prefactor of the exponential asymptotic term in the energy splitting.

a-Lorentz Gauge England.

QED.

COLIN

BAXTER.

Department

of Physics,

University

of Essex, Colchester

CO4

3SQ,

The a-Lorentz gauge is defined as a generalisation of the Lorentz gauge, which contains the Coulomb and usual Lorentz gauges as special cases. A self-consistent formulation of a non-relativistic QED within the a-Lorentz gauge is presented, via the canonical procedure, after the manner of Gupta and Bleuler. This is made possible by the equivalence in the propagation speeds ( = ac) of the longitudinal and scalar photons and results in the identification of the usual Lorentz gauge supplementary condition as being also the quantum analogue of the a-Lorentz gauge condition. The Hamiltonian’s a dependence is superficial and does not influence observables. This is illustrated by a calculation of the hydrogenic Lamb shift. The conditions under which the scalar potential is capable of entering an electromagnetic interaction are investigated.