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Communications in

Mathematical

Physics

Volume 48 1976

Chief Editor J. Glimm, New York, N.Y.

Editorial Board

Advisory Board

H. Araki, Kyoto

G. Gallavotti, Rome

R. Geroch, Chicago, III.

R. Haag, Hamburg

W. Hunziker, Zurich

A. Jaffe, Cambridge, Mass.

J. L. Lebowitz, New York, N.Y.

J. Moser, New York, N.Y.

R. Stora, Marseille

K. Hepp, Zurich

R. Jost, Zurich

M. C. Polivanov, Moscow

D. Ruelle, Bures-sur-Yvette

A. S. Wightman, Princeton, N. J.

Springer-Verlag

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The exclusive copyright for all languages and countries, including the right for photomecha-nical and any other reproductions, also in microform, is transferred to the publisher.

Alle Rechte, einschlieβlich das der Ubersetzung in fremde Sprachen und das der foto-mechanischen Wiedergabe oder einer sonstigen Vervielfaltigung, auch in Mikroform, vor-behalten. Jedoch wird gewerblichen Unternehmen fur den innerbetrieblichen Gebrauch nach Maβgabe des zwischen dem Bόrsenverein des Deutschen Buchhandels e. V. und dem Bundes-verband der Deutschen Industrie abgeschlossenen Rahmenabkommens die Anfertigung einer fotomechanischen Vervielfaltigung gestattet. Wenn fur diese Zeitschrift kein Pauschalabkommen mit dem Verlag vereinbart worden ist, ist eine Wertmarke im Betrage von DM 0,40 pro Seite zu verwenden. Der Verlag la'βt diese Betrage den Autorenverbanden zuflieβen.

Springer-Verlag Berlin Heidelberg New York Printers: Bruhlsche Universitatsdruckerei, Gieβen

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Contents

Adetunji, O.: Remarks on the Wilson-Zimmermann Expansion and Some Properties of the m-Point Distribution . . 199 Aizenman, M., Gallavotti,G., Goldstein, S., Lebowitz,J.L.: Stability and Equilibrium States of

Infinite Classical Systems 1 Baίaban,T., Jezuita, K., Raczka, R.: Second Quantization of Classical Nonlinear Relativistic Field

Theory. Part II. Construction of Relativistic Interacting Local Quantum Field 291 Baumgartner,B.: Thermodynamic Limit of Correlation Functions in a System of Gravitating

Fermions 207 Bergere,M.C, Lam,Y.-M.P.: Zero-Mass Limit in Perturbative Quantum Field Theory . . . . 267 Capocaccia, D.: A Definition of Gibbs State for a Compact Set with Zv Action . . . 85

Evans, D. E.: Positive Linear Maps on Operator Algebras 15 Evans, D.E.: Scattering in the CAR Algebra 23 Gallavotti, G., s. Aizenman, M., et al 1 Georgii,H.-O.: Canonical and Grand Canonical Gibbs States for Continuum Systems . . . . 31 Goldstein, S., s. Aizenman, M., et al 1 Grossmann, A.: Parity Operator and Quantization of ^-Functions 191 Grossmann,A., Seiler,R.: Heat Equation on Phase Space and the Classical Limit of Quantum

Mechanical Expectation Values 195 Holley, R. A., Stroock, D. W.: Applications of the Stochastic Ising Model to the Gibbs S t a t e s . . . 249 Jezuita, K, s. Baϊaban,T, et al 291 Kummer, M.: On Resonant Non Linearly Coupled Oscillators with Two Equal Frequencies . . 53 Lam,Y.-M.P., s. Bergere,M.C 267 Lebowitz,J.L., s. Aizenman, M., et al 1 Lindblad,G.: On the Generators of Quantum Dynamical Semigroups 119 Mardin, A., Streater,R.F.: On the Spinor Rank of Fermi Fields 81 Nakanishi, N.: Complex-dimensional Invariant Delta Functions and Lightcone Singularities . . 97 Nenciu,G.: Self-Adjoίntness and Invariance of the Essential Spectrum for Dirac Operators

Defined as Quadratic Forms 235 Persides,S.: Global Properties of Radial Wave Functions in Schwarzschild's Space-Time. I. The

Regular Singular Points 165 Raczka, R., s. Balaban,T., et al 291 Rouet,A.: Pure Massless Electrodynamics in Veltman's Gauge 89 Ruhl,W., Yunn,B.C.: Operator Product Expansions in Conformally Covariant Quantum Field

Theory 215 Seller, R., s. Grossmann,A 195 SigalJ.M.: On the Discrete Spectrum of the Schrδdinger Operators of Multiparticle Systems 137 SigalJ.M.: On the Point Spectrum of the Schrδdinger Operators of Multiparticle Systems 155 Sirugue, M., s. Sirugue-Collin, M 131 Sirugue-Collin, M., Sirugue, M.: On the Probabilistic Structure of Quasi-free States of a Clifford

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A20414D

CommunicationaJ

Mathe

Volume 48 Number! 1976

Chief Editor J. Glimm, New York, N. Y,

Editorial Board

H. Araki, Kyoto

G. Gallavotti, Rome

R. Geroch, Chicago, III.

R. Haag, Hamburg

W. Hunziker, Zurich

A. Jaffe, Cambridge, Mass.

J. L Lebowitz, New York, N. Y.

J. Moser, New York, N. Y.

R. Stora, Marseille

Advisory Board K. Hepp, Zurich

R. Jost, Zurich

D. Ruelle, Bures-sur-Yvette

M. C. Polivanov, Moscow

A. S. Wightman, Princeton, N. J.

Springer-Verίag

Berlin Heidelberg New York

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Communications in Mathematical Physics

It is a fundamental condition that submitted manuscripts have not been, and will not simul-taneously be submitted or published elsewhere. With the acceptance of a manuscript for publication, the publishers acquire full and exclusive copyright for all languages and countries. Unless special permission has been granted by the publishers, no photographic reproductions,

microform or any other reproductions of a similar nature may be made of the journal, of individual contributions contained therein or of extracts therefrom.

100 offprints of each article will be supplied to the author free-of-charge and additional copies may be obtained at cost price if ordered before the issue goes to press.

Manuscripts may be sent to:

Mathematical methods (Functional analysis, operator algebra and group theory, with direct relevance to physics)

Equilibrium statistical mechanics (Thermodynamic functions, phase transitions, equilibrium states, exactly soluble models)

General relativity

Chief Editor

General structure of quantum field theory and foundations of quantum mechanics

Classical and quantum mechanics of finitely many degrees of freedom

Constructive quantum field theory

Nonequilibrium statistical mechanics (Time devel-opment of infinite systems, ergodic theory, transport theory, random processes, dissipative phenomena) Dynamical systems (Differential equations and their application to physical systems)

Lagrangian quantum field theory Prof. H. Araki, Research Institute for

Math-ematical Sciences, Kyoto University, Kyoto 606, Japan

Prof. G. Gallavotti, Istituto Matematico dell'

Universita, Piazzale delle Scienze, 1 — 00185 Roma, Italy (send registered mail)

Prof. R. Geroch, E. Fermi Institute, University

of Chicago, 933 East 56 Street, Chicago, III. 60637, USA

Prof. J. Glimm, The Rockefeller University,

1230 York Avenue, New York, N.Y. 10021, USA

Prof. R. Haag, II. Institut fϋr Theoretische

Physik, Luruper Chaussee 149, D —2000 Hamburg 50, Federal Republic of Germany

Prof. W. Hunziker, Theoretische Physik, E.T.H.

Zurich, Honggerberg, CH— 8049 Zurich, Switzerland

Prof. A. Jaffe, Lyman Laboratory of Physics,

Harvard University, Cambridge, Mass. 02138, USA

Prof. J. L. Lebowitz, Belfer Graduate School

of Science, Yeshiva University, New York, N.Y. 10033, USA

Prof. J. Moser, New York University, Courant

Institute of Mathematical Sciences, 251 Mercer Street, New York, N. Y. 10012, USA

Prof. R. Stora, Centre National de la

Recherche Scientifique, Centre de Physique Theorique, 31, chemin J. Aiguier, F —13274 Marseille, Cedex, France

In order to avoid delay in publication this journal appears in loose numbers which can be subsequently assembled in volumes.

Subscription Information

Volumes 46 — 51 (3 issues each) will appear in 1976. The publisher reserves the right to issue additional volumes during the calendar year. Information about obtaining back volumes and microform editions available upon request.

North America. Subscription rate: $ 372.40, including postage and handling. Subscriptions are

entered with prepayment only. Orders should be addressed to: Springer-Verlag New York Inc., 175 Fifth Avenue, New York, N.Y. 10010.

Outside North America. Subscription rate: DM 888,—, plus postage and handling. Orders can either

be placed with your bookdealer or sent directly to: Springer-Verlag, Heidelberger Platz 3, D—1000 Berlin 33.

Springer-Verlag

References

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