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Tuesday, July 21, 2020 | History

4 edition of Stochastic Quantization Scheme of Paris and Wu (Monographs and Textbooks in Physical Science Lecture Notes) found in the catalog.

Stochastic Quantization Scheme of Paris and Wu (Monographs and Textbooks in Physical Science Lecture Notes)

by S. Chaturvedi

  • 306 Want to read
  • 24 Currently reading

Published by Amer Inst of Physics .
Written in English

    Subjects:
  • Mathematical Physics,
  • Quantum Theory,
  • Science/Mathematics

  • The Physical Object
    FormatPaperback
    ID Numbers
    Open LibraryOL13431547M
    ISBN 108870882357
    ISBN 109788870882353

    Abstract. We mainly discuss the Parisi-Wu stochastic quantization as a possible stochastic-dynamical approach to quantum mechanics, which gives quantum mechanics by thermal equilibrium limit of a hypothetical stochastic process in a new time other than the ordinary time. The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu.

    Abstract. In these lectures we present an introduction to the method of stochastic quantization due to Parisi and Wu and demonstrate the equivalence between stochastic and canonical methods of quantization in perturbation theory using the techniques due to Floratos and Iliopoulos. is often called a quantizer of X and q(X) a quantization of X. Among all quantizers taking ∗Laboratoire de Probabilit´es et Mod`eles Al´eatoires, CNRS UMR , Universit´e Paris 6, case , 4, pl. Jussieu, F Paris Cedex 5. [email protected] †INRIA, MathFi project and Centre de Math´ematiques, CNRS UMR , Universit´e Paris.

    But even if this point of view is taken for granted, Einstein gravity is far from obsolete, and it is of interest to apply alternative quantization schemes to it. The stochastic quantization method of Parisi and Wu () is particularly attractive, because, in principle, computations of physical quantities can be carried out without ever. About this book Introduction Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well.


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Stochastic Quantization Scheme of Paris and Wu (Monographs and Textbooks in Physical Science Lecture Notes) by S. Chaturvedi Download PDF EPUB FB2

Additional Physical Format: Online version: Chaturvedi, S. Stochastic quantization scheme of Parisi and Wu. Napoli: Bibliopolis, © (OCoLC) This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. Wu in and then developed by many workers.

I assume that the reader has finished a standard. About this book This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. Wu in and then developed by many workers. I assume that the reader has finished a standard course in quantum field : Springer-Verlag Berlin Heidelberg.

We propose a generalization of the euclidean stochastic quantization scheme of Parisi and Wu that is applicable to fields in Minkowski space. A perturbative proof of the equivalence of the new method to ordinary quantization is given for the self-interacting scalar field.

This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. Wu in and then developed by many workers.

I assume that the reader has finished a standard course in quantum field theory. The stochastic quantization scheme of Parisi and Wu exhibits a Euclidean quantum field ψ(x) as the stationary limit with respect to a fictitious time t of the stochastic relaxation process defined for t ≥ 0 by the Langevin equationAuthor: H.

Rumpf. Stochastic quantization schemes of Nelson and Parisi and Wu are applied to a spin-one massive field. Unlike the scalar case Nelson's stochastic spin-one massive field cannot be identified with the corresponding euclidean field even if the fourth component of the euclidean coordinate is taken as equal to the real physical time.

Abstract Stochastic quantization provides a novel and interesting connection between quantum field theory and statistical mechanics, with new applications also in numerical simulations of field theories.

This review article tries to present as broad as possible the most relevant features of the Parisi-Wu approach of stochastic quantization. (Submitted on 31 Oct ) Abstract: The stochastic quantization scheme proposed by Parisi and Wu in is known to have differences from conventional quantum field theory in higher orders.

It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. For a system with generalized coor- dinates qk and described by a lagrangian L, the sto- chastic scheme of Parisi and Wu is based on the Langevin equation ~qk/at = --~SE/Sqk + rlk(t).

(l) Here SE denotes the euclidean action and r/k are gaus- sian white noise sources with (rlk) =. [Show full abstract] interest to apply alternative quantization schemes to it. The stochastic quantization method of Parisi and Wu () is particularly attractive, because, in principle.

Abstract The Parisi-Wu stochastic quantization method is applied to gauge fields and constrained systems. The stochastic quantization scheme of Parisi and Wu has been applied to QED since many years.

Nice agreement with conventional calculations was found in several explicit examples (for reviews see, e.g.,), a general equivalence proof so far was lacking. It is interesting to note that the quantization of the nonlocal fractional fields can also be carried out using the stochastic quantization of Parisi and Wu.

According to this quantization method, one considers Euclidean fields in (d +1)-dimensional space—the usual d -dimensional Euclidean space plus an additional auxiliary time. Within the stochastic quantization scheme of Parisi and Wu [ 1 ] one might be tempted to associate a Langevin equation simply as 1) t ~A (t) +I"(x~ t) (2) (the factor of i derives from having exp(iS) in the conventional Feynman path integral formalism).

Stochastic Quantization, in the sense in which we will use it in this book, is a comparatively new quantization method, which was proposed in by Parisi and Wu [R1]. As it relies strongly on concepts from statistical mechanics and probability theory, it seems appropriate to recall briefly some of the underlying basic aspects.

In the past few years the stochastic quantization method (SQM) proposed by Parisi and Wu [ 1 ] has been extensively developed and applied to many fieldtheoretical problems #`.

In order that SQM may be used for perturbative calculations, it is necessary to have a renormalization scheme for removing the ultraviolet divergences consistently. The electromagnetic field is quantized in the temporal gauge by using the Parisi-Wu stochastic quantization scheme and Nelson's stochastic mechanics.

The stochastic field obtained in the Parisi-Wu. The application of the method of stochastic quantization originally attributed to Parisi and Wu has been extended to spinor fields obeying para‐Fermi statistics. As for fermions (i.e fields associated with particles of half integer spins, like e.g.

electrons) stochastic quantization ideas have been discussed heuristically, after Parisi and Wu seminal paper. The generalizations of the Parisi-Wu stochastic quantization scheme that are necessary for its application to D-dimensional General Relativity are reviewed and some open problems pointed out.Ligang Wu's research works with 6, citations and 4, reads, including: Resilient Distributed Fuzzy Load Frequency Regulation for Power Systems Under Cross-Layer Random Denial-of-Service.A.

Stochastic Gradient Quantization Recently, the topic of stochastic gradient quantization has been attracting growing interests for its being a key approach for improving the communication efficiency of edge learning [6]– [11]. In [6], a scheme called “Quantized SGD” (QSGD) is .