Soloviev, Michael Alexandrovich

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Total publications: 36
Scientific articles: 31
Presentations: 1

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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.


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.


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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. M. A. Soloviev, “Characterization of the Moyal Multiplier Algebras for the Generalized Spaces of Type $S$”, Tr. Mat. Inst. Steklova, 309 (2020),  290–303  mathnet; Proc. Steklov Inst. Math., 309 (2020), 271–283  isi  scopus
2. M. A. Soloviev, “Spaces of Type $S$ as Topological Algebras under Twisted Convolution and Star Product”, Tr. Mat. Inst. Steklova, 306 (2019),  235–257  mathnet  elib; Proc. Steklov Inst. Math., 306 (2019), 220–241  isi  scopus
3. M. A. Soloviev, “Spaces of type $S$ and deformation quantization”, TMF, 201:3 (2019),  315–336  mathnet  elib; Theoret. and Math. Phys., 201:3 (2019), 1682–1700  isi  scopus
4. M. A. Soloviev, “Weyl correspondence for a charged particle in the field of a magnetic monopole”, TMF, 187:2 (2016),  383–398  mathnet  mathscinet  elib; Theoret. and Math. Phys., 187:2 (2016), 782–795  isi  scopus
5. M. A. Soloviev, “Star products on symplectic vector spaces: Convergence, representations, and extensions”, TMF, 181:3 (2014),  568–596  mathnet  mathscinet  elib; Theoret. and Math. Phys., 181:3 (2014), 1612–1637  isi  scopus
6. M. A. Soloviev, “Generalized Weyl correspondence and Moyal multiplier algebras”, TMF, 173:1 (2012),  38–59  mathnet  mathscinet  elib; Theoret. and Math. Phys., 173:1 (2012), 1359–1376  isi  elib  scopus
7. M. A. Soloviev, “Twisted convolution and Moyal star product of generalized functions”, TMF, 172:1 (2012),  9–27  mathnet  mathscinet  elib; Theoret. and Math. Phys., 172:1 (2012), 885–900  isi  elib  scopus
8. M. A. Soloviev, “Noncommutative deformations of quantum field theories, locality, and causality”, TMF, 163:3 (2010),  413–429  mathnet  mathscinet; Theoret. and Math. Phys., 163:3 (2010), 741–752  isi  scopus
9. M. A. Soloviev, “Star product algebras of test functions”, TMF, 153:1 (2007),  3–17  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 153:1 (2007), 1351–1363  isi  scopus
10. M. A. Soloviev, “Decomposition theorems and kernel theorems for a class of functional spaces”, Izv. RAN. Ser. Mat., 70:5 (2006),  199–224  mathnet  mathscinet  zmath  elib; Izv. Math., 70:5 (2006), 1051–1076  isi  elib  scopus
11. M. A. Soloviev, “Axiomatic formulations of nonlocal and noncommutative field theories”, TMF, 147:2 (2006),  257–269  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 147:2 (2006), 660–669  isi  scopus
12. M. A. Soloviev, “Two classes of generalized functions used in nonlocal field theory”, TMF, 143:2 (2005),  195–210  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 143:2 (2005), 651–663  isi  elib
13. M. A. Soloviev, “Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals”, TMF, 128:3 (2001),  492–514  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 128:3 (2001), 1252–1270  isi
14. A. G. Smirnov, M. A. Soloviev, “Wick Power Series Converging to Nonlocal Fields”, TMF, 127:2 (2001),  268–283  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 127:2 (2001), 632–645  isi
15. 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  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 125:1 (2000), 1349–1362  isi
16. A. G. Smirnov, M. A. Soloviev, “Test function space for Wick power series”, TMF, 123:3 (2000),  355–373  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 123:3 (2000), 709–725  isi
17. M. A. Soloviev, “PCT, spin and statistics, and analytic wave front set”, TMF, 121:1 (1999),  139–164  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 121:1 (1999), 1377–1396  isi
18. M. A. Soloviev, “Breaking the space–time translation group in the dipole field model”, TMF, 115:2 (1998),  163–176  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 115:2 (1998), 503–512  isi
19. M. A. Soloviev, “On a spectral condition for infrared singular quantum fields”, TMF, 105:3 (1995),  405–411  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 105:3 (1995), 1520–1524  isi
20. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 34:2 (1994), 263–266  isi
21. V. Ya. Fainberg, M. A. Soloviev, “Nonlocalizability and asymptotical commutativity”, TMF, 93:3 (1992),  514–528  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 93:3 (1992), 1438–1449  isi
22. M. A. Soloviev, “Strengthening of Singer's result on absence of global gauge fixing”, TMF, 78:2 (1989),  163–176  mathnet  mathscinet; Theoret. and Math. Phys., 78:2 (1989), 117–126  isi
23. M. A. Soloviev, “Geometry of classical mechanics with non-Abelian gauge symmetry”, TMF, 73:1 (1987),  3–15  mathnet  mathscinet; Theoret. and Math. Phys., 73:1 (1987), 1019–1028  isi
24. M. A. Soloviev, “Spacelike asymptotic behavior of vacuum expectation values in nonlocal field theory”, TMF, 52:3 (1982),  363–374  mathnet  mathscinet; Theoret. and Math. Phys., 52:3 (1982), 854–862  isi
25. M. A. Soloviev, “A generalization of Ruelle's theorem”, TMF, 52:2 (1982),  213–224  mathnet  mathscinet; Theoret. and Math. Phys., 52:2 (1982), 756–766  isi
26. M. A. Soloviev, “Intersection of Jaffe spaces”, TMF, 45:2 (1980),  147–160  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 45:2 (1980), 941–950  isi
27. M. A. Soloviev, “Relativistically invariant formulation of causality in a nonlocal theory of exponential growth”, TMF, 43:2 (1980),  202–209  mathnet  zmath; Theoret. and Math. Phys., 43:2 (1980), 412–416  isi
28. M. A. Soloviev, “Ruelle's theorem and the theory of quasianalytic classes of functions”, TMF, 42:1 (1980),  3–15  mathnet  mathscinet; Theoret. and Math. Phys., 42:1 (1980), 1–9  isi
29. M. A. Soloviev, “Locality and lattice theory”, TMF, 20:3 (1974),  299–301  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 20:3 (1974), 835–836
30. M. A. Soloviev, “On the Fourier–Laplace transformation of generalized functions”, TMF, 15:1 (1973),  3–19  mathnet  mathscinet; Theoret. and Math. Phys., 15:1 (1973), 317–328
31. M. A. Soloviev, “On the class of distributions compatible with locality”, TMF, 7:2 (1971),  183–191  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 7:2 (1971), 458–464

32. 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  mathnet  elib; Phys. Usp., 60:7 (2017), 743–744  isi
33. 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  mathnet; Phys. Usp., 54:5 (2011), 539–540  isi
34. 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  mathnet; Phys. Usp., 50:7 (2007), 763–765  isi
35. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:2 (2002), 399–405  isi
36. 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  mathnet; Phys. Usp., 40:5 (1997), 545–546  isi

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

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