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Galilee group and liouville equation
ANNALS
OF PHYSICS:
Abstracts
19, 348-319 (1962)
of
Papers
to Appear
in Future
Issues
Theoretical Physics, Universit.y of Vienna, Vienna, Austria The techniques of modern quantum field theory are applied to the electrori-hole fieltl interacting with the field of phonons in a crystal. The interaction is described by the Friihlich Hamiltonian. In the evaluation of the electrical condu&vity, an infinite number of Feynman diagrams has to he taken into account,. The first three of these diagrams art’ worked out explicitly, and are found to he the beginning of a geometrical series, which yields a conductivity -F” for T/B << k0/E~ , -TM5 for k0/E~ << Y/O << 1. For 7’/8 >> 1 1 hr well-known 7’~’ law is reproduced. Galilee Group and IJiol~zlille Equation. A. LOIN~ER, Institute di Pisica dell Ilniversita, Pavia, Italy Within the framework of the Hilbert, space formulation of classical mechanics. we pro! e the following results: (i) the values of the canonical Poisson brackets C:LII be inferred from the post,ulate of the existence of an irreducible Abelian group of unitary ray rotations; (ii) the only irreducible Hilhert representations of the proper (+alilei group which arc cal,able of a physical int,erpretation are those corresponding to the free particle I,iollvillr equation. On (‘omplez CHARAI,
Angular AND
&AN
Momerduw~ .J. SQVIRES,
in Man!/ Lawrence
C’harmel Potentid Scntfering Problum I. JOHN ill. Radiation Laboratory, University of California,
J+rkeley, California A continuation of the S matrix, for many-channel potrritial~sc:atterirlg problems with arbitrar,y spin, awa,y from physical values of the angular momentum, is defined. It is shown that the scntt,ering amplitude can be expressed as a SUIII over physical J values of a sm,,mancl which is meromorphic in the entire finite .I plane. of ,~ll~leon-l~ircleon Scattering in the Strip .4pprosimation lo the Mandrlstam Keprrsedation. JOHN M. CHARAP, Lawrence Radiation J,aboratory, I’niversity of California, Berkeley, California, EMHILVBKIN, l>epartment of Physics, Brown University, Providence, Rhode Island, and ANTONIO S(VTTI, I)epartment of Physics, University of (‘ali fornia, San I>iego, La Jolla, California The nucleon-nucleon scattering amplitude is discussed within the framework of the strip approximation. Asymptotic bounds to the behavior of the amplitudes are derived, and are applied to limit the number of “allowed” single spectral functions to six and corresponding]) to limit t,he t,ypes of dynamically independent, one-particle states. III part,icular, it is found that the pion is in t,his sense allowed, whilst t,he deuteron is not. The unitarity equations, in which only two-particle intercalated states are retained, are explicitly derived in both the N-N and N-i% channels. The N-m equations express a portion of t,he double spectral fun&ons in terms of the ?T-N amplitudes; the S-X equations express another portion of these functions t,hrough coupled integral equations. Theory
348
OF PHYSICS:
Abstracts
19, 348-319 (1962)
of
Papers
to Appear
in Future
Issues
Theoretical Physics, Universit.y of Vienna, Vienna, Austria The techniques of modern quantum field theory are applied to the electrori-hole fieltl interacting with the field of phonons in a crystal. The interaction is described by the Friihlich Hamiltonian. In the evaluation of the electrical condu&vity, an infinite number of Feynman diagrams has to he taken into account,. The first three of these diagrams art’ worked out explicitly, and are found to he the beginning of a geometrical series, which yields a conductivity -F” for T/B << k0/E~ , -TM5 for k0/E~ << Y/O << 1. For 7’/8 >> 1 1 hr well-known 7’~’ law is reproduced. Galilee Group and IJiol~zlille Equation. A. LOIN~ER, Institute di Pisica dell Ilniversita, Pavia, Italy Within the framework of the Hilbert, space formulation of classical mechanics. we pro! e the following results: (i) the values of the canonical Poisson brackets C:LII be inferred from the post,ulate of the existence of an irreducible Abelian group of unitary ray rotations; (ii) the only irreducible Hilhert representations of the proper (+alilei group which arc cal,able of a physical int,erpretation are those corresponding to the free particle I,iollvillr equation. On (‘omplez CHARAI,
Angular AND
&AN
Momerduw~ .J. SQVIRES,
in Man!/ Lawrence
C’harmel Potentid Scntfering Problum I. JOHN ill. Radiation Laboratory, University of California,
J+rkeley, California A continuation of the S matrix, for many-channel potrritial~sc:atterirlg problems with arbitrar,y spin, awa,y from physical values of the angular momentum, is defined. It is shown that the scntt,ering amplitude can be expressed as a SUIII over physical J values of a sm,,mancl which is meromorphic in the entire finite .I plane. of ,~ll~leon-l~ircleon Scattering in the Strip .4pprosimation lo the Mandrlstam Keprrsedation. JOHN M. CHARAP, Lawrence Radiation J,aboratory, I’niversity of California, Berkeley, California, EMHILVBKIN, l>epartment of Physics, Brown University, Providence, Rhode Island, and ANTONIO S(VTTI, I)epartment of Physics, University of (‘ali fornia, San I>iego, La Jolla, California The nucleon-nucleon scattering amplitude is discussed within the framework of the strip approximation. Asymptotic bounds to the behavior of the amplitudes are derived, and are applied to limit the number of “allowed” single spectral functions to six and corresponding]) to limit t,he t,ypes of dynamically independent, one-particle states. III part,icular, it is found that the pion is in t,his sense allowed, whilst t,he deuteron is not. The unitarity equations, in which only two-particle intercalated states are retained, are explicitly derived in both the N-N and N-i% channels. The N-m equations express a portion of t,he double spectral fun&ons in terms of the ?T-N amplitudes; the S-X equations express another portion of these functions t,hrough coupled integral equations. Theory
348