Stochastic Quantization of Gauge Fields

We extend the stochastic quantization procedure of Parisi and Wu to the case of anti-symmetric tensor fields of arbitrary rank. It is shown that the correct number of physical degrees of freedom on mass shell is automatically projected out. The gauge degrees of freedom can be buried in the initial data of the Langevin equation describing the stochastic process in analogy with the treatment of Abelian and non-Abelian gauge fields.

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The extended local gauge invariance and the BRS symmetry in stochastic quantization of gauge fields

Nuclear Physics B ◽

10.1016/0550-3213(90)90517-h ◽

1990 ◽

Vol 335 (3) ◽

pp. 546-568 ◽

Cited By ~ 3

Author(s):

Naohito Nakazawa

Keyword(s):

Gauge Invariance ◽

Gauge Fields ◽

Stochastic Quantization ◽

Local Gauge ◽

Local Gauge Invariance ◽

Brs Symmetry

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Stochastic quantization of Yang-Mills theories coupled with p-form gauge fields

Nuclear Physics B ◽

10.1016/0550-3213(86)90565-1 ◽

1986 ◽

Vol 270 ◽

pp. 507-518 ◽

Cited By ~ 2

Author(s):

Laurent Baulieu

Keyword(s):

Gauge Fields ◽

Stochastic Quantization ◽

Yang Mills

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Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion

International Journal of Modern Physics A ◽

10.1142/s0217751x18500914 ◽

2018 ◽

Vol 33 (16) ◽

pp. 1850091 ◽

Cited By ~ 1

Author(s):

Sung Pil Moon

Keyword(s):

Renormalization Group ◽

Boundary Conditions ◽

General Relation ◽

Scalar Fields ◽

The Other ◽

Gauge Fields ◽

Stochastic Quantization ◽

Massive Fermion ◽

Boundary Terms ◽

Massless Fermions

We examine a suggested relation between stochastic quantization and the holographic Wilsonian renormalization group in the massive fermion case on Euclidean AdS space. The original suggestion about the general relation between the two theories is posted in arXiv:1209.2242 . In the previous researches, it is already verified that scalar fields, U(1) gauge fields, and massless fermions are consistent with the relation. In this paper, we examine the relation in the massive fermion case. Contrary to the other case, in the massive fermion case, the action needs particular boundary terms to satisfy boundary conditions. We finally confirm that the proposed suggestion is also valid in the massive fermion case.

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