Abstract
An attempt is made to study the interaction Hamiltonian,H int =Gψ 2(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 ∼n 6, wheren is the principal quantum number.
Similar content being viewed by others
References
Alabiso C and Schierholz G 1977Nucl. Phys. B126 461
Basu D and Biswas S N 1969J. Math. Phys. 10 2104
Biswas S N, Malik G P and Sudarshan E C G 1972Phys. Rev. D7 2884
Biswas S N, Chaudhuri R N and Malik G P 1973Phys. Rev. D8 1808
Biswas S N, Datta K and Goyal A 1982Phys. Rev. D25 2199
Buchmuller W, Grunberg G and Tye S H H 1980Phys. Rev. Lett. 45 103
Coleman S 1975Lectures given at the Erice Summer School
Eichten E, Gottfried K, Kinoshita T, Lane K D and Yan T M 1978Phys. Rev. D17 3090
Eichten E, Gottfried K, Kinoshita T, Lane K D and Yan T M 1980Phys. Rev. D21 203
Erdelyi A (ed) 1953Higher transcendental functions (Bateman Manuscript Project) (McGraw Hill) vol. II
Gradshteyn I S and Ryzhik I M 1965Table of integrals, series and products (New York: Academic)
Grosse R and Martin A 1980Phys. Rep. 60 341
Henley J R 1979Phys. Rev. D20 2532
Malik G P, Subba Rao J and Johri G 1983Pramana 20 429
Okubo S 1954Prog. Theor. Phys. (Kyoto) 11 80
Pati J C, Salam A and Strathdee J 1981Nucl. Phys. B185 416
Quigg C and Rosener J L 1976Phys. Rep. 56 167
Salam A (Reviewer) 1971Nonpolynomial Lagrangians renormalization and gravity (New York: Gordon and Breach)
Weinberg S and Witten E 1980Phys. Lett. B96 59
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Malik, G.P., Johri, G. Bethe-Salpeter equation with the sine-Gordon interaction. Pramana - J Phys 23, 703–713 (1984). https://doi.org/10.1007/BF02894764
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02894764
Keywords
- Bethe-Salpeter equation
- sine-Gordon interaction
- instantaneous approximation
- Fock’s transformation variables
- Hecke’s theorem
- weak-binding limit
- solitonic kernel
- confinement