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Investigation of the formula for the average of two s-matrix elements in compound nucleus reactions
ANNALSor PHYSICS 167, 224-225 (1986)
Abstracts of Papers to Appear in Future Issues
Infrared Problem in QED and Electric Charge Renormalization. G. MORCHIO. Dipartimento di Fisica dell'UniversitS_, Pisa, italy; AND F. STROCCHI. International School for Advanced Studies, Trieste, Italy. The electric charge renormalization in quantum electrodynamics is discussed, by taking into account the fact that an "infrared dressing transformation" is needed to go from the local states occuring in the Green's functions, to the (physical) charged states which obey the Gauss' law. Apparent difficulties discussed in the literature are resolved. The construction of physical multicharged states is discussed explicitly.
Hidden Supersymmetry and Spectral Asymmetry: Fermion Number Fractionization and Anomalies in Even and Odd Dimensions. R. AKHOURY. Department of Physics, University of California, Los Angeles, California 90024; AYO A. COMT~T. Institut de Physique Nucl6aire, Division de Physique Th6orique, Universit6 Paris Sud, 91400 Orsay, France. We discuss how a "hidden supersymmetry" of the underlying field theories can be used to interpret and to calculate fermion number fractionization, axial anomalies and anomalies in odd dimensions. All of the above effects can be related to a corresponding Witten index A(,6) defined using the hidden supersymmetry--thus providing a unified treatment for them. The relevance of the fl dependence of the Witten index in the different cases is also discussed. Further, for the three-dimensional case, an expression for the parity violating part of the effective action at finite temperatures is obtained.
Investigation of the Formula for the Average of Two S-Matrix Elements in Compound Nucleus Reactions. J. J. M. VERBAARSCHOT. Max-Planck-Institut fiir Kernphysik, Heidelberg, West Germany. Recently the problem of calculating the average of two S-matrix elements describing compound nucleus reactions was solved by using the technique of generating functions and grassmann integration. In this paper we analyze the solution, a 3-dimensional integral, both analytically and numerically. We study the expansion of the integral in powers of the transmission coefficients and the expansion in inverse powers of the transmission coefficients. The former one, which also contains logarithmic terms, is shown to agree with previous work. The latter one is identical to the expansion obtained with the help of the replica trick. After a suitable change of integration variables the integrand becomes finite everywhere in its domain and numerical integration is without any problem. Earlier Monte Carlo calculations are confirmed. The average of two S-matrix elements at the same energy obtained by a Mexican group using general properties of the S-matrix and the maximum entropy principle is shown to coincide with the microscopic result.
Considerations of Polarization in Inclusive Electron Scattering from Nuclei. T. W. DONNELLYAND A. S. RASKIN. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Inclusive electron scattering of either polarized or unpolarized electrons, (e, e') or (e, e'), from polarized nuclei is considered. General forrnulae are given for arbitrary nuclear transitions and
224 0003-4916/86 $7.50 Copyright~ 1986by AcademicPress,Inc. All rightsof reproductionin any formreserved.
Abstracts of Papers to Appear in Future Issues
Infrared Problem in QED and Electric Charge Renormalization. G. MORCHIO. Dipartimento di Fisica dell'UniversitS_, Pisa, italy; AND F. STROCCHI. International School for Advanced Studies, Trieste, Italy. The electric charge renormalization in quantum electrodynamics is discussed, by taking into account the fact that an "infrared dressing transformation" is needed to go from the local states occuring in the Green's functions, to the (physical) charged states which obey the Gauss' law. Apparent difficulties discussed in the literature are resolved. The construction of physical multicharged states is discussed explicitly.
Hidden Supersymmetry and Spectral Asymmetry: Fermion Number Fractionization and Anomalies in Even and Odd Dimensions. R. AKHOURY. Department of Physics, University of California, Los Angeles, California 90024; AYO A. COMT~T. Institut de Physique Nucl6aire, Division de Physique Th6orique, Universit6 Paris Sud, 91400 Orsay, France. We discuss how a "hidden supersymmetry" of the underlying field theories can be used to interpret and to calculate fermion number fractionization, axial anomalies and anomalies in odd dimensions. All of the above effects can be related to a corresponding Witten index A(,6) defined using the hidden supersymmetry--thus providing a unified treatment for them. The relevance of the fl dependence of the Witten index in the different cases is also discussed. Further, for the three-dimensional case, an expression for the parity violating part of the effective action at finite temperatures is obtained.
Investigation of the Formula for the Average of Two S-Matrix Elements in Compound Nucleus Reactions. J. J. M. VERBAARSCHOT. Max-Planck-Institut fiir Kernphysik, Heidelberg, West Germany. Recently the problem of calculating the average of two S-matrix elements describing compound nucleus reactions was solved by using the technique of generating functions and grassmann integration. In this paper we analyze the solution, a 3-dimensional integral, both analytically and numerically. We study the expansion of the integral in powers of the transmission coefficients and the expansion in inverse powers of the transmission coefficients. The former one, which also contains logarithmic terms, is shown to agree with previous work. The latter one is identical to the expansion obtained with the help of the replica trick. After a suitable change of integration variables the integrand becomes finite everywhere in its domain and numerical integration is without any problem. Earlier Monte Carlo calculations are confirmed. The average of two S-matrix elements at the same energy obtained by a Mexican group using general properties of the S-matrix and the maximum entropy principle is shown to coincide with the microscopic result.
Considerations of Polarization in Inclusive Electron Scattering from Nuclei. T. W. DONNELLYAND A. S. RASKIN. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Inclusive electron scattering of either polarized or unpolarized electrons, (e, e') or (e, e'), from polarized nuclei is considered. General forrnulae are given for arbitrary nuclear transitions and
224 0003-4916/86 $7.50 Copyright~ 1986by AcademicPress,Inc. All rightsof reproductionin any formreserved.