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Title: The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field

Abstract

In curved space-time, in order to understand how curved space-time affects the dynamics of scalar and spinning particles, we solve the relativistic particles equations in curved space-time. In the present paper our intention is to solve the (1+1) D Duffin-Kemmer-Petiau (DKP) equation in the background metric ds2=u2(x) (-dt2+dx2). The resulting equation is studied for the special case u(x) = 1 + gx. Finally we discuss the result by comparing with solutions of the Klein-Gordon and the Dirac equations in the presence of background the same metric.

Authors:
; ;  [1]
  1. Mersin University, Department of Physics, Mersin (Turkey)
Publication Date:
OSTI Identifier:
21057106
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 899; Journal Issue: 1; Conference: 6. international conference of the Balkan Physical Union, Istanbul (Turkey), 22-26 Aug 2006; Other Information: DOI: 10.1063/1.2733079; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGY; DIRAC EQUATION; GRAVITATIONAL FIELDS; KLEIN-GORDON EQUATION; METRICS; QUANTUM GRAVITY; RELATIVISTIC RANGE; SCALARS; SPACE-TIME; SPARTICLES

Citation Formats

Havare, A. Kemal, Havare, Ali, and Soeguet, Kenan. The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field. United States: N. p., 2007. Web. doi:10.1063/1.2733079.
Havare, A. Kemal, Havare, Ali, & Soeguet, Kenan. The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field. United States. doi:10.1063/1.2733079.
Havare, A. Kemal, Havare, Ali, and Soeguet, Kenan. Mon . "The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field". United States. doi:10.1063/1.2733079.
@article{osti_21057106,
title = {The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field},
author = {Havare, A. Kemal and Havare, Ali and Soeguet, Kenan},
abstractNote = {In curved space-time, in order to understand how curved space-time affects the dynamics of scalar and spinning particles, we solve the relativistic particles equations in curved space-time. In the present paper our intention is to solve the (1+1) D Duffin-Kemmer-Petiau (DKP) equation in the background metric ds2=u2(x) (-dt2+dx2). The resulting equation is studied for the special case u(x) = 1 + gx. Finally we discuss the result by comparing with solutions of the Klein-Gordon and the Dirac equations in the presence of background the same metric.},
doi = {10.1063/1.2733079},
journal = {AIP Conference Proceedings},
number = 1,
volume = 899,
place = {United States},
year = {Mon Apr 23 00:00:00 EDT 2007},
month = {Mon Apr 23 00:00:00 EDT 2007}
}
  • A brief review of two-body Dirac and Kemmer-Duffin-Petiau approaches for the bound state problem of two fermions is presented from an algebraic point of view in a comparative manner. Reduction of the direct product of two Dirac spaces is discussed. 12 refs.
  • We lay down the formalism for the treatment of pionic atoms level widths and shifts using the Kemmer-Duffin-Petiau equation. Interactions are introduced in a Lorentz invariant way. An analytical transformation is shown that connects between different sets of interactions. The Kisslinger potential is obtained as a special case of a scalar-tensor optical potential. Results are shown in the accompanying paper.
  • The introduction of scalar interactions in the Kemmer-Duffin-Petiau equation induces the appearance of Darwin terms in the effective Klein-Gordon equation that resemble the Ericson-Ericson Lorentz-Lorenz effect in pion-nucleus scattering. The xi/sub ..pi../ parameter turns out to be xi/sub ..pi../approx.2 in agreement with recent calculations of the effect.
  • Fits to data on strong interaction level shifts and widths in pionic atoms, over the whole of the periodic table, are made with the Kemmer-Duffin-Petiau equation. Comparisons are made with the conventional Klein-Gordon equation and emphasis is placed on the problem of anomalously small shifts and widths. The Kemmer-Duffin-Petiau equation yields fits which are marginally better than those obtained with the Klein-Gordon equation.
  • A simple exact analytical solution of the relativistic Duffin-Kemmer-Petiau equation within the framework of the asymptotic iteration method is presented. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the Coulomb potentials. As a nontrivial example, the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method.