# Four-Gauge-Particle Scattering Amplitudes and Polyakov String Path Integral in the proper-time gauge

## TL;DR

This paper computes four-gauge-particle scattering amplitudes using the Polyakov string path integral in the proper-time gauge, revealing alpha prime corrections and tachyon poles, which are relevant for understanding string effects beyond field theory.

## Contribution

It introduces a novel approach to evaluate string scattering amplitudes in the proper-time gauge, systematically incorporating alpha prime corrections and analyzing their differences from conventional methods.

## Key findings

- Proper-time gauge yields amplitudes with alpha prime corrections.
- Amplitudes contain tachyon poles consistent with three-particle scattering.
- Proper-time gauge approach may better explore string corrections and high-energy behavior.

## Abstract

We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include $\ap$-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corrections become relevant with finite $\ap$, the scattering amplitude in the proper-time gauge differs from the conventional one: The Polyakov string path integral in the proper-time gauge, equivalent to the deformed cubic string field theory, systematically provides the alpha prime corrections. In addition, we find that the scattering amplitude in the proper-time gauge contains tachyon poles in a manner consistent with three-particle-scattering amplitudes. The scattering amplitudes evaluated using the Polyakov string path integral in the proper-time gauge may be more suitable than conventional ones for exploring string corrections to the quantum field theories and high energy behaviors of open string.