Abstract
In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator overline{varPsi}varPsi between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator overline{varPsi}varPsi is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.
Highlights
Of diagonal matrix elements is a much simpler task than that of the non-diagonal ones
On the one hand we would like to demonstrate that the light-cone lattice approach admits an appropriate framework for computing the finite volume form factors of the Massive Thirring model and on the other hand we would like to give further justification for the validity of the LeClair-Mussardo type series representation conjectured in [17]
That in the continuum limit, when the lattice constant tends to zero, the leading order divergence arising in the fermionic expectation values of Ψ Ψ is of the same form as that expected from the renormalization group analysis of the Massive Thirring model
Summary
Where m0 and g denotes the bare mass and the coupling constant of the theory, respectively. Throughout the paper we use the chiral representation for the fermions as follows: Ψ=. It is well known [32], that this fermion model can be mapped to the sine-Gordon (SG). The perturbing operator cos(βΦ) of the SG model is related to the trace of the stress-energy tensor ΘT as follows:. From (2.5) and (2.6) the fermion bilinear can be expressed in terms of the trace of the stress-energy tensor as follows:. From (2.8) it can be seen that the matrix elements of Ψ Ψ are divergent in the attractive regime (β2 < 4π) and the operator valued coefficient of the leading order divergence in a is proportional to the trace of the stress-energy tensor.. From (2.8) it can be seen that the matrix elements of Ψ Ψ are divergent in the attractive regime (β2 < 4π) and the operator valued coefficient of the leading order divergence in a is proportional to the trace of the stress-energy tensor. In this paper we show that our light-cone lattice computations account for the scaling behavior (2.8) and up to a constant factor, allow one to compute the diagonal matrix elements of ΘT
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