Generalized Stochastic Quantization of Yang–Mills Theory

Hüffel, H.; Kelnhofer, Gerald

doi:10.1006/aphy.1998.5851

Cited by 19 publications

(39 citation statements)

References 22 publications

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“…As already indicated in [1] these structures can equally be translated into the original field space A. With the help of the partition of unity the locally defined densities µ α as well as e −S tot α can be pieced together to give a globally well defined twisted top form Ω on A…”

Section: Global Path Integralmentioning

confidence: 99%

“…It is our aim to discuss a globally valid path integral procedure for the quantization of Yang-Mills theory based on a recently introduced generalization [1][2][3][4] of the Parisi-Wu stochastic quantization scheme [5][6][7]; for different globally valid stochastic interpretations of the Faddeev-Popov procedure [8] see [9,10].…”

Section: Mathematical Settingmentioning

confidence: 99%

“…It is well known that such a procedure breaks down in the case of gauge theories, as due to the gauge invariance no normalizable equilibrium limit emerges. A generalization of the Parisi-Wu scheme was introduced in [14] and extended recently in [1] by performing special, geometrically distinguished modifications of both the drift and diffusion terms such that -most essentially-all expectation values of gauge invariant observables are left unchanged. This lead to a well defined Fokker-Planck formulation and the equilibrium density was derivable straightforwardly.…”

Section: Generalized Stochastic Quantizationmentioning

confidence: 99%

“…To the density µ α there is associated a corresponding twisted top form on Γ α ×G which for simplicity we denote by the same symbol. Using for convenience a matrix representation of G α [1] we straightforwardly verify that…”

Section: Global Path Integralmentioning

confidence: 99%

See 3 more Smart Citations

Quantizing Yang-Mills theory: From Parisi-Wu stochastic quantization to a global path integral

Hüffel¹,

Kelnhofer

2000

Nuclear Physics B - Proceedings Supplements

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Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole space of gauge potentials is shortly reviewed; in the following we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme. MATHEMATICAL SETTINGIt is our aim to discuss a globally valid path integral procedure for the quantization of YangMills theory based on a recently introduced generalization [1-4] of the Parisi-Wu stochastic quantization scheme [5][6][7]; for different globally valid stochastic interpretations of the Faddeev-Popov procedure [8] see [9,10].Let P (M, G) be a principal fiber bundle with compact structure group G over the compact Euclidean space time M . Let A denote the space of all irreducible connections on P and let G denote the gauge group, which is given by all vertical automorphisms on P reduced by the centre of G. Then G acts freely on A and defines a principal Gfibration A π −→ A/G =: M over the paracompact [11] space M of all inequivalent gauge potentials with projection π. Due to the Gribov ambiguity [12] the principal G-bundle A → M is not globally trivializable.From [11] it follows that there exists a locally finite open cover U = {U α } of M together with a set of background gauge fields {A (α) 0 ∈ A} such that Γ α = {B ∈ π −1 (U α )|D *

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Section: Global Path Integralmentioning

confidence: 99%

Section: Mathematical Settingmentioning

confidence: 99%

Section: Generalized Stochastic Quantizationmentioning

confidence: 99%

Section: Global Path Integralmentioning

confidence: 99%

See 2 more Smart Citations

Quantizing Yang-Mills theory: From Parisi-Wu stochastic quantization to a global path integral

Hüffel¹,

Kelnhofer

2000

Nuclear Physics B - Proceedings Supplements

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“…It is our aim to present a quite different argumentation based on a recently introduced generalization [6,7] of the stochastic quantization scheme [8,9,10].…”

mentioning

confidence: 99%

Global path integral quantization of Yang–Mills theory

Hüffel¹,

Kelnhofer²

2000

Physics Letters B

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Based on a generalization of the stochastic quantization scheme recently a modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory was derived, the modification consisting in the presence of specific f inite contributions of the pure gauge degrees of freedom. Due to the Gribov problem the gauge fixing can be defined only locally and the whole space of gauge potentials has to be partitioned into patches. We propose a global path integral density for the Yang-Mills theory by summing over all patches, which can be proven to be manifestly independent of the specific local choices of patches and gauge fixing conditions, respectively. In addition to the formulation on the whole space of gauge potentials we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme and to a proposal of Stora, respectively.

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On the Geometry of Gauge Field Theories

Hüffel

Kelnhofer

Springer Proceedings in Physics

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Generalized Stochastic Quantization of Yang–Mills Theory

Cited by 19 publications

References 22 publications

Quantizing Yang-Mills theory: From Parisi-Wu stochastic quantization to a global path integral

Quantizing Yang-Mills theory: From Parisi-Wu stochastic quantization to a global path integral

Global path integral quantization of Yang–Mills theory

On the Geometry of Gauge Field Theories

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