Applications of Thirring Model to Inhomogenous Rolling Tachyon and Dissipative Quantum Mechanics

TL;DR

This paper employs the Thirring model with boundary mass to analyze inhomogeneous rolling tachyon dynamics and dissipative quantum mechanics, revealing conditions for the tachyon's time evolution and constructing boundary states for quantum systems.

Contribution

It extends the Thirring model to include boundary mass for modeling inhomogeneous tachyon evolution and constructs boundary states for dissipative quantum systems.

Findings

Time evolution of inhomogeneous tachyon occurs only when 2/√3 < R < 2.

Constructed boundary states describe dissipative quantum systems at critical and off-critical points.

The model provides insights into unstable D-brane decay processes.

Abstract

We study the rolling tachyon and the dissipative quantum mechanics using the Thirring model with a boundary mass. We construct a boundary state for the dissipative quantum system in one dimension, which describes the system at the off-critical points as well as at the critical point. Then we extend the Thirring model with a boundary mass in order to depict the time evolution of an unstable D-branes with one direction wrapped on a circle of radius $R$, which is termed the inhomogeneous rolling tachyon. The analysis based on the Thirring model shows that the time dependent evolution of the inhomogeneous tachyon is possible only when $\frac{2}{\sqrt{3}}< R < 2$.