Derivation of a Generalized Stochastic Path-Integral Formulation Based on Ito Chalculus

Kawara, Hideyo; Namiki, Mikio; Okamoto, H.; Tanaka, Satoshi

doi:10.1143/ptp/84.4.749

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A Generating Functional For Dynamic Correlation Functions1

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2009

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Cited by 6 publications

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“…Before doing that, we derive a path integral representation for Z d . Although we will not follow their work directly, see [11] for a discussion of path integral representations of generating functionals based on Ito discretization and [12] for continuum formulation. By definition, Z d is an average over the probability density functions of the Gaussian random variables,…”

Section: A Generating Functional For Dynamic Correlation Functionsmentioning

confidence: 99%

Effective potential for complex Langevin equations

Guralnik

Pehlevan

2009

Nuclear Physics B

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Section: A Generating Functional For Dynamic Correlation Functionsmentioning

confidence: 99%

Effective potential for complex Langevin equations

Guralnik

Pehlevan

2009

Nuclear Physics B

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Stochastic quantization of bottomless systems based on a kerneled Langevin equation

et al. 1992

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Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

1993

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We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to O(N ) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variablesis, actually equivalent to the one in the general-coordinate-transformation-covariant and vielbein-rotationinvariant formalism. * To be published in Nucl. Phys. B -1 -

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Derivation of a Generalized Stochastic Path-Integral Formulation Based on Ito Chalculus

Cited by 6 publications

References 1 publication

Effective potential for complex Langevin equations

Effective potential for complex Langevin equations

Stochastic quantization of bottomless systems based on a kerneled Langevin equation

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

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