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

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