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TMF, 1999, Volume 119, Number 2, Pages 345–352 (Mi tmf743)  

This article is cited in 12 scientific papers (total in 12 papers)

Gaussian functional integrals and Gibbs equilibrium averages

D. P. Sankovich

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We show that Gibbs equilibrium averages of Bose-operators can be represented as path integrals over a special Gauss measure defined in the corresponding space of continuous functions. This measure arises in the Bogoliubov $T$-product approach and is non-Wiener.

DOI: https://doi.org/10.4213/tmf743

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English version:
Theoretical and Mathematical Physics, 1999, 119:2, 670–675

Bibliographic databases:

Received: 08.10.1998
Revised: 01.12.1998

Citation: D. P. Sankovich, “Gaussian functional integrals and Gibbs equilibrium averages”, TMF, 119:2 (1999), 345–352; Theoret. and Math. Phys., 119:2 (1999), 670–675

Citation in format AMSBIB
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\paper Gaussian functional integrals and Gibbs equilibrium averages
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 119
\issue 2
\pages 670--675
\crossref{https://doi.org/10.1007/BF02557358}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. P. Sankovich, “Some Properties of Functional Integrals with Respect to the Bogoliubov Measure”, Theoret. and Math. Phys., 126:1 (2001), 121–135  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. D. P. Sankovich, “Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory”, Theoret. and Math. Phys., 127:1 (2001), 513–527  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245  mathnet  mathscinet  zmath
    4. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357  mathnet  crossref  crossref  adsnasa  isi
    6. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    7. Sankovich D.P., “Gibbs Equilibrium Averages and Bogolyubov Measure”, Problems of Atomic Science and Technology, 2012, no. 1, 248–252  isi
    8. Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Theory Probab. Appl., 57:1 (2013), 60–81  mathnet  crossref  crossref  zmath  isi  elib  elib
    9. V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, Theoret. and Math. Phys., 173:3 (2012), 1720–1733  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    10. A. I. Nazarov, R. S. Pusev, “Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms”, St. Petersburg Math. J., 25:3 (2014), 455–466  mathnet  crossref  mathscinet  zmath  isi  elib
    11. V. R. Fatalov, “Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional”, Theoret. and Math. Phys., 191:3 (2017), 870–885  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Nazarov A.I. Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55  crossref  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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