Michael A. Soloviev
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Michael A. Soloviev has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
V. Ya. Fainberg
Department of Theoretical Physics P.N.Lebedev Physical Institute Leninsky prospect, 53, 117924, Moscow, Russia
2 shared publicationsA. G. Smirnov
Lebedev Physics Institute, RAS
1 shared publication- Alexander G. Smirnov
I. E. Tamm Theory Department, P. N. Lebedev Physical Institute, Leninsky Prospect 53, Moscow 119991, Russia
1 shared publication V.Ya Fainberg
I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Academy of Sciences of the USSR, Moscow B-333, USSR
1 shared publication
Latest Publications
- 28 August 2021
- Published by Springer Nature in Integral Equations and Operator Theory
- Vol. 93 (5) , 1-32
Inclusion Theorems for the Moyal Multiplier Algebras of Generalized Gelfand–Shilov Spaces
- 28 August 2021
- Published by Springer Nature in Integral Equations and Operator Theory
- Vol. 93 (5) , 1-32
Inclusion Theorems for the Moyal Multiplier Algebras of Generalized Gelfand–Shilov Spaces
- Open Access
Inclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces
We prove that the Moyal multiplier algebras of the generalized Gelfand-Shilov spaces of type $S$ contain Palamodov spaces of type $\mathcal E$ and the inclusion maps are continuous. We also give a direct proof that the Palamodov spaces are algebraically and topologically isomorphic to the strong duals of the spaces of convolutors for the corresponding spaces of type $S$. The obtained results provide an effective way to describe the properties of pseudodifferential operators with symbols in the spaces of type $\mathcal E$.Open AccessInclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces
We prove that the Moyal multiplier algebras of the generalized Gelfand-Shilov spaces of type $S$ contain Palamodov spaces of type $\mathcal E$ and the inclusion maps are continuous. We also give a direct proof that the Palamodov spaces are algebraically and topologically isomorphic to the strong duals of the spaces of convolutors for the corresponding spaces of type $S$. The obtained results provide an effective way to describe the properties of pseudodifferential operators with symbols in the spaces of type $\mathcal E$. - 1 May 2020
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 309 (1) , 271-283
Characterization of the Moyal Multiplier Algebras for the Generalized Spaces of Type S
We investigate the properties of the Moyal multiplier algebras for the generalized Gelfand-Shilov spaces \(S_{{a_k}}^{{b_n}}\). We prove that these algebras contain Palamodov spaces of type \({\mathscr{E}}\), and establish continuity properties of the operators with Weyl symbols in this class. Analogous results are obtained for the projective version of the spaces of type S and are extended to the multiplier algebras for various translation-invariant star products.- 1 May 2020
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 309 (1) , 271-283
Characterization of the Moyal Multiplier Algebras for the Generalized Spaces of Type S
We investigate the properties of the Moyal multiplier algebras for the generalized Gelfand-Shilov spaces \(S_{{a_k}}^{{b_n}}\). We prove that these algebras contain Palamodov spaces of type \({\mathscr{E}}\), and establish continuity properties of the operators with Weyl symbols in this class. Analogous results are obtained for the projective version of the spaces of type S and are extended to the multiplier algebras for various translation-invariant star products.- 1 December 2019
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 201 (3) , 1682-1700
Spaces of Type S and Deformation Quantization
We study the properties of the Gelfand-Shilov spaces [equation]in the context of deformation quantization. Our main result is a characterization of their corresponding multiplier algebras with...
- 1 December 2019
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 201 (3) , 1682-1700
Spaces of Type S and Deformation Quantization
We study the properties of the Gelfand-Shilov spaces [equation]in the context of deformation quantization. Our main result is a characterization of their corresponding multiplier algebras with...
- 1 September 2019
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 306 (1) , 220-241
Spaces of Type S as Topological Algebras under Twisted Convolution and Star Product
The properties of the generalized Gelfand-Shilov spaces [equation] are studied from the viewpoint of deformation quantization. We specify the conditions on the defining sequences ( a k) and ( b n)...
- 1 September 2019
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 306 (1) , 220-241
Spaces of Type S as Topological Algebras under Twisted Convolution and Star Product
The properties of the generalized Gelfand-Shilov spaces [equation] are studied from the viewpoint of deformation quantization. We specify the conditions on the defining sequences ( a k) and ( b n)...
- Open Access
Dirac's magnetic monopole and the Kontsevich star product
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant $\hbar$. We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich's graphs.Open AccessDirac's magnetic monopole and the Kontsevich star product
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant $\hbar$. We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich's graphs. - Open Access
Integral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators
A new integral representation is obtained for the star product corresponding to the $s$-ordering of the creation and annihilation operators. This parametric ordering convention introduced by Cahill and Glauber enables one to vary the type of ordering in a continuous way from normal order to antinormal order. Our derivation of the corresponding integral representation is based on using reproducing formulas for analytic and antianalytic functions. We also discuss a different representation whose kernel is a generalized function and compare the properties of this kernel with those of the kernels of another family of star products which are intermediate between the $qp-$ and $pq$-quantization.Open AccessIntegral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators
A new integral representation is obtained for the star product corresponding to the $s$-ordering of the creation and annihilation operators. This parametric ordering convention introduced by Cahill and Glauber enables one to vary the type of ordering in a continuous way from normal order to antinormal order. Our derivation of the corresponding integral representation is based on using reproducing formulas for analytic and antianalytic functions. We also discuss a different representation whose kernel is a generalized function and compare the properties of this kernel with those of the kernels of another family of star products which are intermediate between the $qp-$ and $pq$-quantization. - 6 February 2018
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 51 (9) , 095205
Dirac’s magnetic monopole and the Kontsevich star product
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant ħ . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.
- 6 February 2018
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 51 (9) , 095205
Dirac’s magnetic monopole and the Kontsevich star product
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant ħ . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.
- Open Access
Dirac's monopole, quaternions, and the Zassenhaus formula
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
Open AccessDirac's monopole, quaternions, and the Zassenhaus formula
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
- 23 November 2016
- Published by American Physical Society (APS) in Physical Review D
- Vol. 94 (10) , 105021
Dirac’s monopole, quaternions, and the Zassenhaus formula
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant ℏ. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
- 23 November 2016
- Published by American Physical Society (APS) in Physical Review D
- Vol. 94 (10) , 105021
Dirac’s monopole, quaternions, and the Zassenhaus formula
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant ℏ. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.