The Faddeev–Jackiw Approach and the Conformal Affine sl(2) Toda Model Coupled to the Matter Field

Abstract The conformal affine sl (2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev–Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry.

[1]  G. Takács,et al.  Non-unitarity in quantum affine Toda theory and perturbed conformal field theory , 1998, hep-th/9810006.

[2]  J. Klauder,et al.  Solving Gauge Invariant Systems without Gauge Fixing: The Physical Projector in 0+1 Dimensional Theories , 1998, hep-th/9809119.

[3]  J. Pons,et al.  Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories , 1996, hep-th/9610067.

[4]  L. A. Ferreira,et al.  Affine Toda systems coupled to matter fields , 1995, hep-th/9512105.

[5]  C. Wotzasek.  Faddeev-Jackiw approach to hidden symmetries , 1995, hep-th/9502042.

[6]  M. Noga,et al.  First-order Lagrangians and the Hamiltonian formalism , 1994 .

[7]  C. Wotzasek,et al.  Faddeev-Jackiw Quantization of Non-Abelian Systems , 1993 .

[8]  H. Montani.  SYMPLECTIC ANALYSIS OF CONSTRAINED SYSTEMS , 1993 .

[9]  L. A. Ferreira,et al.  Hirota's solitons in the affine and the conformal affine Toda models , 1992, hep-th/9212086.

[10]  L. A. Ferreira,et al.  Connection between the affine and conformal affine Toda models and their Hirota solution , 1992, hep-th/9207061.

[11]  J. Barcelos-Neto,et al.  SYMPLECTIC QUANTIZATION OF CONSTRAINED SYSTEMS , 1992 .

[12]  J. Govaerts.  HAMILTONIAN REDUCTION OF FIRST-ORDER ACTIONS , 1990 .

[13]  L. Bonora,et al.  Conformal affine sl2 Toda field theory , 1990 .

[14]  R. Jackiw,et al.  Hamiltonian reduction of unconstrained and constrained systems. , 1988, Physical review letters.

[15]  W. Siegel.  Manifest Lorentz invariance sometimes requires non-linearity☆ , 1984 .

[16]  E. Witten.  Chiral symmetry, the 1/N expansion and the SU(N) thirring model , 1978 .

[17]  D. Olive,et al.  Magnetic monopoles as gauge particles , 1977 .

[18]  S. Orfanidis,et al.  Soliton solutions of the massive thirring model , 1975 .

[19]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[20]  R. E. Casten,et al.  Nuclear Physics , 1935, Nature.