On Field Theories of Loops

Details On Field Theories of Loops On Field Theories of Loops

1994-11-30

arxiv.org/abs/hep-th/9411232v2

Mod.Phys.Lett. A10 (1995) 2175

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTex, final version to be published in Modern Physics Letters A

Scientific paper

10.1142/S0217732395002337

We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in a field theory of loops. The corresponding Fokker-Planck hamiltonian defines a non-critical string field theory. We study both orientable and non-orientable interactions of loops in terms of matrix models and take the continuum limit for one-matrix case. As a consequence, we show the equivalence of stochastic quantization of matrix models in loop space to the transfer-matrix formalism in dynamical triangulation of random surfaces. We also clarifies the origin of Virasoro algebra in this context.

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