Quantum Corrections in Collective Field Theory

TL;DR

This paper reviews and extends the calculation of tachyon scattering amplitudes in the $c=1$ matrix model using a finite prescription for the collective field Hamiltonian, and confirms the exactness of the cubic Hamiltonian through loop correction comparisons.

Contribution

It introduces a finite prescription for the collective field Hamiltonian and demonstrates the equivalence of loop corrections with the fermionic picture, supporting the Hamiltonian's exactness.

Findings

Loop corrections match between collective field theory and fermionic picture.

The cubic Hamiltonian is confirmed to be exact.

A finite prescription for the collective field Hamiltonian is proposed.

Abstract

We review and extend the computation of scattering amplitudes of tachyons in the $c=1$ matrix model using a manifestly finite prescription for the collective field hamiltonian. We give further arguments for the exactness of the cubic hamiltonian by demonstrating the equality of the loop corrections in the collective field theory with those calculated in the fermionic picture.