### Abstract

In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. However a broader framework, which we call“bulk quantization”, is required for extension to fermions, and for the increased power afforded by the higher symmetry of the 5-dimensional action that is topological when expressed in terms of auxiliary fields. Within the broader framework, we give a direct proof by means of Schwinger-Dyson equations that a time-slice of the 5-dimensional theory is equivalent to the usual 4-dimensional theory. The proof does not rely on the conjecture that the relevant stochastic process relaxes to an equilibrium distribution. Rather, it depends on the higher symmetry of the 5-dimensional action which includes a BRST-type topological invariance, and invariance under translation and inversion in the 5-th time. We express the physical S-matrix directly in terms of the truncated 5-dimensional correlation functions, for which “going off the mass-shell” means going from the 3 physical degrees of freedom to 5 independent variables. We derive the Landau-Cutokosky rules of the 5-dimensional theory which include the physical unitarity relation.

Original language | English (US) |
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Pages (from-to) | 1-24 |

Number of pages | 24 |

Journal | Journal of High Energy Physics |

Volume | 5 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 2001 |

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### Keywords

- BRST Quantization
- Non-perturbative Effects
- QCD
- Renormalization Regularization and Renormalons

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*5*(8), 1-24. https://doi.org/10.1088/1126-6708/2001/08/016