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Soloviev, Michael Alexandrovich

 Statistics Math-Net.Ru Total publications: 36 Scientific articles: 31 Presentations: 1

 Number of views: This page: 837 Abstract pages: 8880 Full texts: 3407 References: 1173
Senior Researcher
Doctor of physico-mathematical sciences (1991)
Speciality: 01.04.02 (Theoretical physics)
Birth date: 13.09.1944
E-mail: ,
Keywords: functional analysis, topological vector spaces, distributions, hyperfunctions, analytic functionals, spectral analysis of singularities, fibre bundles, quantum field theory, gauge symmetry.

Subject:

The theory of Fourier&ndash';Laplace transformation was developed for the functionals defined on the Gelfand–Shilov spaces of type S and the corresponding generalization of Vladimirov's theorems on functions holomorphic in tubular cones was obtained. The existence of smallest carrier cones was proved for the analytic functionals belonging to the classes $(S^\alpha)'$ and $(S^\alpha_\beta)'$, $\alpha<1$, and analogues of some basic structure theorems (including density and decomposition theorems) of the theory of hyperfunctions were established for these classes. The theory of Lorentz-covariant distributions was extended to ultradistributions, hyperfunctions and analytic functionals. The test function space $S^1_1$ corresponding to Fourier hyperfunctions was proposed as a universal object for formulating local quantum field theory (QFT). An abstract version of Ruelle's theorem on cluster decomposition properties of vacuum expectation values of quantum fields was formulated and proved by using the theory of quasianalytic classes. Namely, if two distributions coincide in an open cone and the supports of their Fourier transforms are separated by a nonzero distance, then both of them have an exponential decrease of order $\geq 1$ inside this cone. An extension of this theorem to analytic functionals was applied to construct the space of scattering states and the scattering matrix for nonlocal interactions of particles. An axiomatic formulation of nonlocal QFT was developed in terms of operator-valued highly singular generalized functions and a new derivation of the spin-statistics relation and CPT symmetry was presented. This derivation covers nonlocal fields and is based on exploiting the notion of analytic wave front set. A simple and general method for the operator realization of Wick-ordered entire functions of the indefinite metric free fields in Fock–Hilbert–Krein space was developed through the use of an appropriate generalization of the Paley–Wiener–Schwartz theorem. A number of papers were devoted to an comparative analysis of the topological obstructions to globally fixing the gauge in non-Abelian gauge theories and in string theory and also to an investigation of geometrical and functional-analytic structure of the infinite-dimensional principle bundle determined by the action of the group of gauge transformations on gauge fields. For non-Abelian gauge theory, the principle bundle was shown to be irreducible to a finite-dimensional subgroup. It was proved that, after an invariant regularization suppressing the ultraviolet divergences, the Gaussian measure of the functional integrals of Yang–Mills theory is supported by those function classes that admit a local gauge choice.

Biography

Graduated from Faculty of Physics of M. V. Lomonosov Moscow State University (MSU) in 1965 (department of quantum field theory). Ph. D. thesis was defended in 1978. D. Sci. thesis was defended in 1991. The list of my works contains more than 50 titles. Since 1994 I have headed the elementary particle theory section of I. E. Tamm Department of Theoretical Physics of P. N. Lebedev Physical Institute.

Member of Moscow Mathematical Society, RFBR Grants No. 96-01-00105 and No. 99-01-00376.

Main publications:
• Soloviev M.A. Beyond the theory of hyperfunctions, in: "Developments in Mathematics: The Moscow School", V. Arnold and M. Monastyrsky (eds.). London: Chapman and Hall, 1993, 131-193.
• Soloviev M.A. An extension of distribution theory and of the Paley-Wiener-Schwartz theorem related to quantum gauge theory. Commun. Math. Phys., 1997, 184, 579-596.
• Soloviev M.A. Wick-ordered entire functions of the indefinite metric free field. Lett. Math. Phys., 1997, 41, 265-277.

http://www.mathnet.ru/eng/person17947
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/189938

Publications in Math-Net.Ru
 2019 1. M. A. Soloviev, “Spaces of Type $S$ as Topological Algebras under Twisted Convolution and Star Product”, Tr. Mat. Inst. Steklova, 306 (2019),  235–257  ; Proc. Steklov Inst. Math., 306 (2019), 220–241 2. M. A. Soloviev, “Spaces of type $S$ and deformation quantization”, TMF, 201:3 (2019),  315–336  ; Theoret. and Math. Phys., 201:3 (2019), 1682–1700 2016 3. M. A. Soloviev, “Weyl correspondence for a charged particle in the field of a magnetic monopole”, TMF, 187:2 (2016),  383–398      ; Theoret. and Math. Phys., 187:2 (2016), 782–795 2014 4. M. A. Soloviev, “Star products on symplectic vector spaces: Convergence, representations, and extensions”, TMF, 181:3 (2014),  568–596      ; Theoret. and Math. Phys., 181:3 (2014), 1612–1637 2012 5. M. A. Soloviev, “Generalized Weyl correspondence and Moyal multiplier algebras”, TMF, 173:1 (2012),  38–59      ; Theoret. and Math. Phys., 173:1 (2012), 1359–1376 6. M. A. Soloviev, “Twisted convolution and Moyal star product of generalized functions”, TMF, 172:1 (2012),  9–27      ; Theoret. and Math. Phys., 172:1 (2012), 885–900 2010 7. M. A. Soloviev, “Noncommutative deformations of quantum field theories, locality, and causality”, TMF, 163:3 (2010),  413–429    ; Theoret. and Math. Phys., 163:3 (2010), 741–752 2007 8. M. A. Soloviev, “Star product algebras of test functions”, TMF, 153:1 (2007),  3–17        ; Theoret. and Math. Phys., 153:1 (2007), 1351–1363 2006 9. M. A. Soloviev, “Decomposition theorems and kernel theorems for a class of functional spaces”, Izv. RAN. Ser. Mat., 70:5 (2006),  199–224        ; Izv. Math., 70:5 (2006), 1051–1076 10. M. A. Soloviev, “Axiomatic formulations of nonlocal and noncommutative field theories”, TMF, 147:2 (2006),  257–269        ; Theoret. and Math. Phys., 147:2 (2006), 660–669 2005 11. M. A. Soloviev, “Two classes of generalized functions used in nonlocal field theory”, TMF, 143:2 (2005),  195–210        ; Theoret. and Math. Phys., 143:2 (2005), 651–663 2001 12. M. A. Soloviev, “Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals”, TMF, 128:3 (2001),  492–514        ; Theoret. and Math. Phys., 128:3 (2001), 1252–1270 13. A. G. Smirnov, M. A. Soloviev, “Wick Power Series Converging to Nonlocal Fields”, TMF, 127:2 (2001),  268–283      ; Theoret. and Math. Phys., 127:2 (2001), 632–645 2000 14. A. G. Smirnov, M. A. Soloviev, “Spectral properties of Wick power series for a free field with an indefinite metric”, TMF, 125:1 (2000),  57–73      ; Theoret. and Math. Phys., 125:1 (2000), 1349–1362 15. A. G. Smirnov, M. A. Soloviev, “Test function space for Wick power series”, TMF, 123:3 (2000),  355–373      ; Theoret. and Math. Phys., 123:3 (2000), 709–725 1999 16. M. A. Soloviev, “PCT, spin and statistics, and analytic wave front set”, TMF, 121:1 (1999),  139–164      ; Theoret. and Math. Phys., 121:1 (1999), 1377–1396 1998 17. M. A. Soloviev, “Breaking the space–time translation group in the dipole field model”, TMF, 115:2 (1998),  163–176      ; Theoret. and Math. Phys., 115:2 (1998), 503–512 1995 18. M. A. Soloviev, “On a spectral condition for infrared singular quantum fields”, TMF, 105:3 (1995),  405–411      ; Theoret. and Math. Phys., 105:3 (1995), 1520–1524 1994 19. A. V. Krasnozhon, Yu. D. Pletner, M. A. Solov'ev, “The propagation of a quasifront in a stratified rotating fluid”, Zh. Vychisl. Mat. Mat. Fiz., 34:2 (1994),  310–314      ; Comput. Math. Math. Phys., 34:2 (1994), 263–266 1992 20. V. Ya. Fainberg, M. A. Soloviev, “Nonlocalizability and asymptotical commutativity”, TMF, 93:3 (1992),  514–528      ; Theoret. and Math. Phys., 93:3 (1992), 1438–1449 1989 21. M. A. Soloviev, “Strengthening of Singer's result on absence of global gauge fixing”, TMF, 78:2 (1989),  163–176    ; Theoret. and Math. Phys., 78:2 (1989), 117–126 1987 22. M. A. Soloviev, “Geometry of classical mechanics with non-Abelian gauge symmetry”, TMF, 73:1 (1987),  3–15    ; Theoret. and Math. Phys., 73:1 (1987), 1019–1028 1982 23. M. A. Soloviev, “Spacelike asymptotic behavior of vacuum expectation values in nonlocal field theory”, TMF, 52:3 (1982),  363–374    ; Theoret. and Math. Phys., 52:3 (1982), 854–862 24. M. A. Soloviev, “A generalization of Ruelle's theorem”, TMF, 52:2 (1982),  213–224    ; Theoret. and Math. Phys., 52:2 (1982), 756–766 1980 25. M. A. Soloviev, “Intersection of Jaffe spaces”, TMF, 45:2 (1980),  147–160      ; Theoret. and Math. Phys., 45:2 (1980), 941–950 26. M. A. Soloviev, “Relativistically invariant formulation of causality in a nonlocal theory of exponential growth”, TMF, 43:2 (1980),  202–209    ; Theoret. and Math. Phys., 43:2 (1980), 412–416 27. M. A. Soloviev, “Ruelle's theorem and the theory of quasianalytic classes of functions”, TMF, 42:1 (1980),  3–15    ; Theoret. and Math. Phys., 42:1 (1980), 1–9 1974 28. M. A. Soloviev, “Locality and lattice theory”, TMF, 20:3 (1974),  299–301      ; Theoret. and Math. Phys., 20:3 (1974), 835–836 1973 29. M. A. Soloviev, “On the Fourier–Laplace transformation of generalized functions”, TMF, 15:1 (1973),  3–19    ; Theoret. and Math. Phys., 15:1 (1973), 317–328 1971 30. M. A. Soloviev, “On the class of distributions compatible with locality”, TMF, 7:2 (1971),  183–191      ; Theoret. and Math. Phys., 7:2 (1971), 458–464 2017 31. B. M. Bolotovskii, M. A. Vasiliev, B. L. Voronov, A. V. Gurevich, K. P. Zybin, N. S. Kardashev, A. I. Nikishov, M. A. Solov'ev, S. M. Stishov, I. V. Tyutin, V. E. Fortov, A. E. Shabad, “Vladimir Ivanovich Ritus (on his 90th birthday)”, UFN, 187:7 (2017),  799–800    ; Phys. Usp., 60:7 (2017), 743–744 2011 32. E. G. Bonner, M. A. Vasil'ev, B. L. Voronov, B. B. Govorkov, I. M. Dremin, R. E Kallosh, L. V. Keldysh, V. I. Ritus, V. P. Silin, M. A. Solov'ev, I. V. Tyutin, A. E. Shabad, “In memory of Vladimir Yakovlevich Fainberg”, UFN, 181:5 (2011),  563–564  ; Phys. Usp., 54:5 (2011), 539–540 2007 33. B. M. Bolotovskii, M. A. Vasiliev, B. L. Voronov, V. L. Ginzburg, A. V. Gurevich, N. S. Kardashev, A. A. Komar, L. V. Keldysh, A. I. Nikishov, M. A. Soloviev, I. V. Tyutin, A. E. Shabad, “Vladimir Ivanovich Ritus (on his eightieth birthday)”, UFN, 177:7 (2007),  801–802  ; Phys. Usp., 50:7 (2007), 763–765 2002 34. D. V. Anosov, V. L. Ginzburg, A. B. Zhizhchenko, M. I. Monastyrskii, S. P. Novikov, Ya. G. Sinai, M. A. Soloviev, “Naum Natanovich Meiman (obituary)”, Uspekhi Mat. Nauk, 57:2(344) (2002),  179–184      ; Russian Math. Surveys, 57:2 (2002), 399–405 1997 35. M. A. Vasiliev, V. L. Ginzburg, A. V. Gurevich, G. F. Zharkov, N. S. Kardashov, L. V. Keldysh, D. A. Kirzhnits, A. I. Nikishov, M. A. Soloviev, I. V. Tyutin, E. L. Feinberg, I. S. Shapiro, “Vladimir Ivanovich Ritus (on his seventieth birthday)”, UFN, 167:5 (1997),  569–570  ; Phys. Usp., 40:5 (1997), 545–546

Presentations in Math-Net.Ru
 1 Deformation quantization and the spaces of type SM. A. Soloviev Internaional conference «Modern Mathematical Physics. Vladimirov-95»November 14, 2018 12:30

Organisations