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    • Bethe-Salpeter equation with the sine-Gordon interaction

      G P Malik Gautam Johri

      Particle Physics Volume 23 Issue 6 December 1984 pp 703-713

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    • Keywords

       

      Bethe-Salpeter equation; sine-Gordon interaction; instantaneous approximation; Fock’s transformation variables; Hecke’s theorem; weak-binding limit; solitonic kernel; confinement

    • Abstract

       

      An attempt is made to study the interaction Hamiltonian,Hint =Gψ2(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit. We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n6, wheren is the principal quantum number.

    • Author Affiliations

       

      G P Malik1 Gautam Johri1 2

      1. School of Environmental Sciences, Jawaharlal Nehru University, New Delhi - 110 067, India
      2. Department of Physics and Astrophysics, University of Delhi, Delhi - 110 007, India

    • Dates

       
      Published
      December 1984
      Manuscript received
      25 February 1984
      Manuscript revised
      22 June 1984

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