Abstract
We discuss a few new results within the exactly solvable relativistic models studied in both the conventional and the light front field theory. The models include the Rothe–Stamatescu, the Thirring, the Federbush and the Thirring–Wess model. The unifying feature is that the corresponding field equations are solved in a simple and exact form. We work within the hamiltonian framework and pay a careful attention to the correct definition of interacting currents which are built from the known solutions in a point-split regularized manner. Quantum “anomalies” follow immediately. The Hamiltonians of the models are expressed in terms of the correct (dynamically independent) field variables, namely the free Heisenberg fields. Due to the simplicity of the models’ dynamics, one can explicitly determine structure of the physical ground states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Thirring W.E.: A soluble relativistic field theory?. Ann. Phys. 3, 91–112 (1958)
Schwinger J.: Gauge invariance and mass. II. Phys. Rev. 128, 2425–2429 (1962)
Schroer B.: Infrateilchen in Quantenfeldtheorie. Fort. der Physik 11, 1–31 (1963)
Wightman, A.S.: Introduction to Some Aspects of the Relativistic Dynamics of Quantized Fields. In: Cargese Lectures in Theoretical Physics, Gordon and Breach, New York, pp. 171–291 (1967)
Lowenstein J.H., Swieca J.A.: Quantum electrodynamics in two dimensions. Ann. Phys. 68, 172–195 (1971)
Abdalla E., Abdalla M.C.B., Rothe K.D.: Nonperturbative Methods in Two-Dimensional Quantum Field Theory. World Scientific, Singapore (1991)
Strocchi F.: General Properties of Quantum Field Theory. World Scientific, Singapore (1993)
Rothe K.D., Stamatescu I.O.: Study of a two-dimensional model with axial-current-pseudoscalar derivative interaction. Ann. Phys. 95, 202–244 (1975)
Thirring W., Wess J.: Solution of a field theory model in one time and one space dimensions. Ann. Phys. 27, 331–337 (1964)
Federbush K.: A two-dimensional relativistic field theory. Phys. Rev. 121, 1247–1249 (1961)
Martinovic L., Grangé P.: Hamiltonian formulation of exactly solvable models and their physical vacuum states. Phys. Lett. B 724, 310–315 (2013)
Mutet B., Grangé P., Werner E.: Taylor–Lagrange renormalization and gauge theories in four dimensions. J. Phys. A 45, 315401–315425 (2012)
Martinovic L.: New operator solution of the Schwinger model in a covariant gauge and axial anomaly. Acta Phys. Polon. Supp. 6, 287–294 (2013)
Belvedere L.V., Rodrigues A.F.: The Thirring interaction in the two-dimensional axial-current–pseudoscalar derivative coupling model. Ann. Phys. 321, 2793–2809 (2006)
Klaiber, B.: The Thirring model. In: Lectures in Theoretical Physics, Vol. Xa, New York, pp. 141–176 (1968)
Coleman S.: The quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088–2122 (1975)
Faber M., Ivanov A.N.: On the equivalence between sine-Gordon model and Thirring model in the chirality broken phase of the Thirring model. Eur. Phys. J. C 20, 723–757 (2001)
Mattis D.C., Lieb E.H.: Exact solution of a many fermion system and its associated bose field. Math. Phys. 6, 304–312 (1965)
Fujita, T., Hiramoto, M., Homma, T., Takahashi, H.: New vacuum of the Bethe ansatz solution in Tirring model. J. Phys. Soc. Jpn. 74, 1143–1149 (2005) hep-th/0410221
Martinovic, L., Grangé P.: (unpublished)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Martinovic̆, L. Solvable Models in the Conventional and Light-Front Field Theory: Recent Progress. Few-Body Syst 55, 527–534 (2014). https://doi.org/10.1007/s00601-014-0896-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-014-0896-1