First-Order Lagrangians and Path-Integral Quantization in the t-J Model

Details First-Order Lagrangians and Path-Integral Quantization in the t-J Model First-Order Lagrangians and Path-Integral Quantization in the t-J Model

1999-03-16

arxiv.org/abs/cond-mat/9903249v1

Physics

Condensed Matter

latex file, to appear in Ann. Phys. (NY)

Scientific paper

10.1006/aphy.1999.5930

By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the Hubbard ${\hat X}$-operators are used as field variables. In this framework, we first study the spinless fermion model which satisfies the graded algebra spl(1,1). Later on, in order to satisfy the Hubbard ${\hat X}$-operators commutation rules satisfiying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for the t-J model are found. This model is also analyzed in the context of the path- integral formalism, and so the correlation generating functional and the effective Lagrangian are constructed.

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