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

TL;DR

This paper develops a first-order Lagrangian and path-integral framework for the t-J model using supersymmetric symplectic formalism and Hubbard operators, providing new insights into its constrained dynamics and quantization.

Contribution

It introduces a novel first-order constrained Lagrangian formalism for the t-J model using supersymmetric methods and Hubbard operators, advancing the quantization approach.

Findings

Derived a family of first-order constrained Lagrangians for the t-J model.

Analyzed the model using path-integral formalism to construct correlation functions.

Identified the necessary constraints to satisfy graded algebra commutation rules.

Abstract

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.