Summary
The construction of a relativistic quantum field theory for the Thirring model is performed by applying the Hamiltonian formalism. The construction is conceptually very natural and makes use of the exact solution of the Luttinger model. The equivalence between the Thirring model and the Luttinger model, until now stated by heuristic methods, is proved in a rigorous way in the sense that the limit of infinite box, zero Fermi momentum and local interaction of renormalized Luttinger-model Schwinger functions exists and verifies the equations that are usually required to be satisfied by the Thirring-model Schwinger functions.
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References
W. Thirring:Ann. Phys. (N.Y.),3, 91 (1958).
F. L. Scarf andJ. Wess:Nuovo Cimento,26, 150 (1962).
A. S. Wightmansc:Cargese Lectures on Physics (1964).
L. Garding andJ. L. Lions:Nuovo Cimento,14, 45 (1959).
B. Klaiber:Helv. Phys. Acta,37, 554 (1964).
R. F. Streater andA. S. Wightman:Spin, Statistics and All That (Benjamin, New York, N.Y., 1964).
B. Klaiber:Lectures at Summer Institute for Theoretical Physics, University of Colorado, edited byA. Barutsc andW. Brittinsc (Gordon and Breach, New York, N.Y., 1968).
K. Ostertwalder andR. Schrader:Commun. Math. Phys.,31, 83 (1972).
J. Luttinger:J. Math. Phys.,4, 1154 (1963).
D. Mattis andE. Lieb:J. Math. Phys.,6, 304 (1965).
G. Benfatto, G. Gallavotti andV. Mastropietro:Phys. Rev. B,45, 5468 (1992).
A. Theunmann:J. Math. Phys.,8, 2460 (1967).
K. Johnson:Nuovo Cimento,20, 773 (1961).
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Mastropietro, V. Schwinger functions in Thirring and Luttinger models. Nuov Cim B 108, 1095–1107 (1993). https://doi.org/10.1007/BF02827305
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DOI: https://doi.org/10.1007/BF02827305