Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator reduced Salpeter equation
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)
A popular three-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all bound-state constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of the problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state solutions correspond to real discrete spectra bounded from below and are thus free of all instabilities.
- OSTI ID:
- 21024093
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 76, Issue 12; Other Information: DOI: 10.1103/PhysRevD.76.125028; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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