Igor V. Volovich

  • L. Accardi
  • B. Dragovich
  • M. O. Katanaev
  • A. Yu. Khrennikov
  • V. V. Kozlov
  • S. V. Kozyrev
  • F. Murtagh
  • M. Ohya
  • V. S. Varadarajan
  • V. S. Vladimirov
Review Articles


We present a brief review of the scientific work and achievements of Igor V. Volovich on the occasion of his 65th birthday.

Key words

I. V. Volovich theoretical physics mathematical physics mathematics 


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  1. 1.
    V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (World Scientific, Singapore, 1994).Google Scholar
  2. 2.
    L. Accardi, Yu. G. Lu and I. V. Volovich, Quantum Theory and Its Stochastic Limit (Springer-Verlag, 2002).Google Scholar
  3. 3.
    M. Ohya and I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-Systems (Springer, Dordrecht, 2011).zbMATHCrossRefGoogle Scholar
  4. 4.
    I. V. Volovich, “p-Adic string,” Class. Quant. Grav. 4, L83–L87 (1987).MathSciNetCrossRefGoogle Scholar
  5. 5.
    I. V. Volovich, “Number theory as the ultimate physical theory,” p-Adic Numb. Ultr. Anal. Appl. 2(1), 77–87 (2010).MathSciNetCrossRefGoogle Scholar
  6. 6.
    B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev and I. V. Volovich, “On p-adicmathematical physics,” p-Adic Numb. Ultr.Anal. Appl. 1(1), 1–17 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    I.V. Volovich, “Randomness in classicalmechanics and quantum mechanics,” Found. Phys. 41(3), 516–528 (2011).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    I. V. Volovich, “Bogoliubov equations and functional mechanics,” Theor. Math. Phys. 164(3), 1128–1135 (2010).CrossRefGoogle Scholar
  9. 9.
    A. S. Trushechkin and I. V. Volovich, “Functional classicalmechanics and rational numbers,” p-Adic Numb. Ultr. Anal. Appl. 1(4), 361–367 (2009).MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. N. Pechen, I. V. Volovich, “Quantum multipole noise and generalized quantum stochastic equations,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5(4), 441–464 (2002).MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    V. S. Vladimirov and I. V. Volovich, “Superanalysis. I. Differential calculus,” Theor. Math. Phys. 59(1), 317–335 (1984); “Superanalysis. II. Integral calculus,” Theor. Math. Phys. 60 (2), 743–765 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    V. S. Vladimirov and I. V. Volovich, “TheWiener-Hopf equation, the Riemann-Hilbert problem and orthogonal polynomials,” Sov. Math. Dokl. 26, 415–419 (1982).zbMATHGoogle Scholar
  13. 13.
    I. Ya. Aref’eva, B. G. Dragovic and I.V. Volovich, “Extra time-like dimensions lead to a vanishing cosmological constant,” Phys. Lett. B 177,3–4, 357–360 (1986).MathSciNetGoogle Scholar
  14. 14.
    I. Ya. Aref’eva, B. Dragovich, P. H. Frampton and I. V. Volovich, “The wave function of the universe and p-adic gravity,” Int. J. Mod. Phys. A 6(24), 4341–4358 (1991).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    M. Ohya and I. V. Volovich, “New quantum algorithm for studying NP-complete problems,” Rep. Math. Phys. 52(1), 25–33 (2003).MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    I. Volovich, “Quantum cryptography in space and Bell’s theorem, Foundations of probability and physics,” QP-PQ: Quantum Probab.White Noise Anal. 13, 364–372 (World Sci. Publ., River Edge, NJ, 2001).Google Scholar
  17. 17.
    A. Khrennikov and I. Volovich, “Local realism, contextualism and loopholes in Bell’s experiments,” Foundations of Probability and Physics 2 (Växjö, 2002); Math. Model. Phys. Eng. Cogn. Sci. 5, 325–343 (Växjö Univ. Press, Växjö, 2003).Google Scholar
  18. 18.
    V.V. Kozlov and I.V. Volovich, “Finite action Klein-Gordon solutions on Lorentzianmanifolds,” Int. J. Geom. Methods Mod. Phys. 3(7), 1349–1357 (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    M.O. Katanaev and I. V. Volovich, “Theory of defects in solids and three-dimensional gravity,” Ann. Physics 216(1), 1–28 (1992).MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    I. Ya. Aref’eva, K. S. Viswanathan and I. V. Volovich, “Planckian-energy scattering, colliding plane gravitational waves and black hole creation,” Nuclear Phys. B 452(1–2), 346–366 (1995).MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    A. Borowiec, M. Francaviglia and I. Volovich, “Topology change and signature change in non-linear firstorder gravity,” Int. J. Geom. Methods Mod. Phys. 4(4), 647–667 (2007).MathSciNetCrossRefGoogle Scholar
  22. 22.
    S. V. Kozyrev and I. V. Volovich, “The Arrhenius formula in kinetic theory andWitten’s spectral asymptotics,” J. Phys. A: Math. Gen. 44(21), 215–202 (2011).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • L. Accardi
    • 1
  • B. Dragovich
    • 2
  • M. O. Katanaev
    • 3
  • A. Yu. Khrennikov
    • 4
  • V. V. Kozlov
    • 3
  • S. V. Kozyrev
    • 3
  • F. Murtagh
    • 5
  • M. Ohya
    • 6
  • V. S. Varadarajan
    • 7
  • V. S. Vladimirov
    • 3
  1. 1.University of Roma “Tor Vergata”RomaItaly
  2. 2.Institute of PhysicsUniversity of BelgradeBelgradeSerbia
  3. 3.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  4. 4.International Center for Mathematical Modelling in Physics and Cognitive SciencesLinnaeus UniversityVäxjö-KalmarSweden
  5. 5.Science Foundation IrelandWilton Park HouseDublin 2Ireland
  6. 6.Department of Information SciencesTokyo University of ScienceNoda-shi, ChibaJapan
  7. 7.Department ofMathematicsUCLALos AngelesUSA

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