skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Optical theorem in N dimensions

Abstract

The quantum-mechanical optical theorem in N-dimensional space is derived in a simple way from S-matrix theory.

Authors:
 [1]
  1. Institute of Radiophysics and Electronics, Armenian Academy of Sciences, Ashtarak-2, 378410 (Armenia)
Publication Date:
OSTI Identifier:
20786390
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.064701; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; MANY-DIMENSIONAL CALCULATIONS; OPTICAL THEOREM; QUANTUM MECHANICS; S MATRIX; SPACE

Citation Formats

Hovakimian, L. B. Optical theorem in N dimensions. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Hovakimian, L. B. Optical theorem in N dimensions. United States. doi:10.1103/PHYSREVA.72.0.
Hovakimian, L. B. Thu . "Optical theorem in N dimensions". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786390,
title = {Optical theorem in N dimensions},
author = {Hovakimian, L. B.},
abstractNote = {The quantum-mechanical optical theorem in N-dimensional space is derived in a simple way from S-matrix theory.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • We study the Levinson theorem for a Dirac particle in an n-dimensional central field by use of the Green function approach, based on an analysis of the n-dimensional radial Dirac equation obtained through a simple algebraic derivation. We show that the zero-momentum phase shifts are related to the number of bound states with |E|<m plus the number of half-bound states of zero momenta--i.e., |E|=m--which are denoted by finite, but not square-integrable, wave functions.
  • Gauge theories of quarks which possess approximate chiral SU(3) x SU(3) symmetry also have approximate U(3) x U(3) symmetry. If the axial symmetries are realized in the Goldstone mode, then one would naively expect a fourth SU(3) singlet pseudoscalar meson with mass comparable to that of the pion. This is contrary to experiment. It has been argued, however, that quark confinement can remove the unwanted Goldstone boson from the physical spectrum of the theory. It is the purpose of this article to shed light on this phenomenon by studying it in a simple setting. We consider the sigma model withmore » minimal electrodynamic coupling in 1+1 dimensions. We confirm that the singlet Goldstone boson is indeed absent although the axial symmetry is spontaneously broken. The would-be massless meson gains a mass from the long-range interactions responsible for confinement. If the Abelian gauge coupling is set to zero, the axial symmetry is no longer spontaneously broken. Using equivalent-boson methods a simple proof of the equivalence of the nonlinear sigma model and the Thirring model (with an additional decoupled massless field) is presented. (AIP)« less
  • A general critical state model describes the field and current distributions in a hard Type II superconductor with a local relation between the field and current density. We show here that such models cannot provide a magnetically shielded region in superconducting wires in zero applied field.
  • The comment by Baixeras et al. (J. Appl. Phys. 52, 4330 (1981)) on the recent paper by Migliori (J. Appl. Phys. 51, 3439 (1980)) utilizes counterexamples not consistent with Migliori's premise. Baixeras et al. also fail to support their contention that in two dimensions it is possible, if more difficult, to solve a general critical state model with boundary conditions.
  • In an attempt to clarify the controversial views about the general validity of the rather frequently and successfully used critical state mode, we consider an explicit formulation of this model and present a careful analysis of the boundaries of the regions where the field B is zero. As a result, it seems that the arguments recently published that call into question the general validity of this mode are not acceptable.