S matrix of collective field theory

TL;DR

This paper computes the S matrix in collective field theory using LSZ formalism, revealing boundary condition-dependent proportionalities and providing formulas for general potentials, including a case linked to a naked singularity.

Contribution

It introduces explicit formulas for the S matrix in collective field theory under different boundary conditions, expanding understanding of scattering in these models.

Findings

S matrices are proportional to momenta or energies depending on boundary conditions.

Derived simple formulas for S matrices with general potentials at order g_st^2.

Calculated the S matrix for a potential related to a naked singularity.

Abstract

By applying the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism, we study the S matrix of collective field theory in which fermi energy is larger than the height of potential. We consider the spatially symmetric and antisymmetric boundary conditions. The difference is that S matrices are proportional to momenta of external particles in antisymmetric boundary condition, while they are proportional to energies in symmetric boundary condition. To the order of $g_{st}^2$, we find simple formulas for the S matrix of general potential. As an application, we calculate the S matrix of a case which has been conjectured to describe a "naked singularity".