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Non perturbative methods in quantum theory and QFT and their application to actual physical problems

Abstract

The aim of the project is two-fold. We shall develop the methods of quantum theory and also apply these methods to some interesting problems of modern physics. A considerable part of the project is dedicated to non perturbative quantum electrodynamics. The cases of strong external field and of non-linear quantum theory will be treated in detail. The prominent place occupied by this topic is related to its' role in the front-line physics research including the physics of dense stars and hadronic matter, as well as the physics of graphene. The physics of new materials - graphene, topological insulators and Weyl semimetals - is considered in separate Chapter in this project. The spectrum of excitations in these materials is described by the Dirac equation, which makes Quantum Field Theory the most adequate theoretical tool and connects this research to other parts of the project. Most of our calculations here (the Casimir effect, optical properties, conductivity) will admit immediate experimental verification. The holographic principle has less connections with the current experiments, but no less interesting. Though this principle was suggested in String Theory, our consideration has a broader context. We shall analyze many, mostly low-dimensional, holographic models and check their consistency. The practical tool here is non-perturbative (in the AdS radius) calculations in QFT, similar to the rest of the project. The part related to noncommutative geometry is on the cross-road with pure mathematics: we shall use the advances in mathematics (as the deformation quantization and formality) to address physics problems and utilize the QFT techniques for the purposes of mathematics. (AU)

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Scientific publications (64)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BORDAG, M.; FIALKOVSKY, I; KHUSNUTDINOV, N.; VASSILEVICH, D.. Bulk contributions to the Casimir interaction of Dirac materials. Physical Review B, v. 104, n. 19, . (16/03319-6, 19/10719-9)
HERZOG, CHRISTOPHER P.; HUANG, KUO-WEI; VASSILEVICH, DMITRI V.. Interface conformal anomalies. Journal of High Energy Physics, n. 10, . (16/03319-6)
AFSHAR, HAMID; GONZALEZ, HERNAN A.; GRUMILLER, DANIEL; VASSILEVICH, DMITRI. Flat space holography and the complex Sachdev-Ye-Kitaev model. Physical Review D, v. 101, n. 8, . (16/03319-6)
ALONSO-IZQUIERDO, A.; FRESNEDA, RODRIGO; MATEOS GUILARTE, J.; VASSILEVICH, D.. Soliton fermionic number from the heat kernel expansion. EUROPEAN PHYSICAL JOURNAL C, v. 79, n. 6, . (17/50294-1, 16/03319-6)
ECKER, FLORIAN; VALCARCEL, CARLOS; VASSILEVICH, DMITRI. 2D holography beyond the Jackiw-Teitelboim model. Journal of High Energy Physics, n. 9, . (16/03319-6)
ANDRIANOV, ALEXANDER; SOLDATI, ROBERTO; VASSILEVICH, DMITRI. Emission of Photons by Quasiparticles in Weyl Semimetals. SYMMETRY-BASEL, v. 12, n. 5, . (14/23772-1, 16/03319-6)
EMELIANOVA, N.; FIALKOVSKY, V, I.; KHUSNUTDINOV, N.. Casimir effect for biaxial anisotropic plates with surface conductivity. MODERN PHYSICS LETTERS A, v. 35, n. 3, SI, . (19/10719-9, 19/06033-4, 16/03319-6)
VASSILEVICH, DMITRI. On the (im)possibility of Casimir repulsion between Chern-Simons surfaces. MODERN PHYSICS LETTERS A, v. 35, n. 3, SI, . (16/03319-6)
KHUSNUTDINOV, N.; EMELIANOVA, N.. Low-temperature expansion of the Casimir-Polder free energy for an atom interacting with a conductive plane. International Journal of Modern Physics A, v. 34, n. 2, . (17/50294-1, 16/03319-6)
FIALKOVSKY, I.; KURKOV, M.; VASSILEVICH, D.. Quantum Dirac fermions in a half-space and their interaction with an electromagnetic field. Physical Review D, v. 100, n. 4, . (17/50294-1, 16/03319-6)
KHUSNUTDINOV, NAIL. Self-action in gravity. EUROPEAN PHYSICAL JOURNAL PLUS, v. 136, n. 6, . (19/10719-9, 16/03319-6)
CARDENAS, MARCELA; FUENTEALBA, OSCAR; GONZALEZ, HERNAN A.; GRUMILLER, DANIEL; VALCARCEL, CARLOS; VASSILEVICH, DMITRI. Boundary theories for dilaton supergravity in 2D. Journal of High Energy Physics, n. 11, . (16/03319-6)
KHUSNUTDINOV, NAIL; KASHAPOV, RASHID; WOODS, LILIA M.. Thermal Casimir and Casimir-Polder interactions in N parallel 2D Dirac materials. 2D MATERIALS, v. 5, n. 3, . (17/50294-1, 16/03319-6)
GAVRILOV, S. P.; GITMAN, D. M.; SHISHMAREV, A. A.. States of charged quantum fields and their statistical properties in the presence of critical potential steps. Physical Review A, v. 99, n. 5, . (16/03319-6)
KURKOV, MAXIM; VASSILEVICH, DMITRI. Gravitational parity anomaly with and without boundaries. Journal of High Energy Physics, n. 3, . (16/03319-6, 15/05120-0)
MATEOS GUILARTE, J.; VASSILEVICH, D.. Fractional fermion number and Hall conductivity of domain walls. Physics Letters B, v. 797, . (17/50294-1, 16/03319-6)
BORDAG, M.; FIALKOVSKY, I.; VASSILEVICH, D.. Casimir interaction of strained graphene. Physics Letters A, v. 381, n. 30, p. 2439-2443, . (16/03319-6)
KURKOV, M.; VASSILEVICH, D.. Parity anomaly in four dimensions. Physical Review D, v. 96, n. 2, . (16/03319-6, 15/05120-0)
ASSIRATI, J. L. M.; GITMAN, D. M.. Covariant quantizations in plane and curved spaces. EUROPEAN PHYSICAL JOURNAL C, v. 77, n. 7, . (16/03319-6)
FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; VASSILEVICH, DMITRI. Quest for Casimir repulsion between Chern-Simons surfaces. Physical Review B, v. 97, n. 16, . (17/50294-1, 16/03319-6)
ADORNO, T. C.; FERREIRA, R.; GAVRILOV, S. P.; GITMAN, D. M.. Role of switching-on and -off effects in the vacuum instability. International Journal of Modern Physics A, v. 33, n. 11, . (16/03319-6)
VASSILEVICH, DMITRI; COSTA OLIVEIRA, FERNANDO MARTINS. Nearly associative deformation quantization. LETTERS IN MATHEMATICAL PHYSICS, v. 108, n. 10, p. 2293-2301, . (16/03319-6)
ADORNO, T. C.; GAVRILOV, S. P.; GITMAN, D. M.. Violation of vacuum stability by inverse square electric fields. EUROPEAN PHYSICAL JOURNAL C, v. 78, n. 12, . (16/03319-6)
MARKOV, YU. A.; MARKOVA, M. A.; GITMAN, D. M.. Unitary Quantization and Para-Fermi Statistics of Order 2. JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS, v. 127, n. 3, p. 398-421, . (16/03319-6)
RAIMUNDO, K.; BALDIOTTI, M. C.; FRESNEDA, R.; MOLINA, C.. Classical-quantum correspondence for two-level pseudo-Hermitian systems. Physical Review A, v. 103, n. 2, . (16/03319-6)
GAVRILOV, S. P.; GITMAN, D. M.; SHISHMAREV, A. A.. States of charged quantum fields and their statistical properties in the presence of critical potential steps. HYSICAL REVIEW, v. 99, n. 5, p. 23-pg., . (16/03319-6)
BAGROV, V. G.; GITMAN, D. M.; SHISHMAREV, A. A.; FARIAS JR, A. J. D.. Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems. JOURNAL OF SYNCHROTRON RADIATION, v. 27, p. 10-pg., . (16/03319-6)
IVANOV, A., V; KURKOV, M. A.; VASSILEVICH, D. V.. Heat kernel, spectral functions and anomalies in Weyl semimetals. Journal of Physics A-Mathematical and Theoretical, v. 55, n. 22, p. 19-pg., . (16/03319-6)
KURKOV, MAXIM; VASSILEVICH, DMITRI. Gravitational parity anomaly with and without boundaries. Journal of High Energy Physics, v. N/A, n. 3, p. 17-pg., . (15/05120-0, 16/03319-6)
FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; VASSILEVICH, DMITRI. Quest for Casimir repulsion between Chern-Simons surfaces. PHYSICAL REVIEW B, v. 97, n. 16, p. 11-pg., . (17/50294-1, 16/03319-6)
VASSILEVICH, DMITRI. Index theorems and domain walls. Journal of High Energy Physics, v. N/A, n. 7, p. 13-pg., . (17/50294-1, 16/03319-6)
EMELIANOVA, N.; FIALKOVSKY, I., V; KHUSNUTDINOV, N.. Casimir effect for biaxial anisotropic plates with surface conductivity. MODERN PHYSICS LETTERS A, v. 35, n. 3, p. 5-pg., . (19/06033-4, 19/10719-9, 16/03319-6)
HERZOG, CHRISTOPHER P.; HUANG, KUO-WEI; VASSILEVICH, DMITRI V.. Interface conformal anomalies. Journal of High Energy Physics, v. N/A, n. 10, p. 14-pg., . (16/03319-6)
GRUMILLER, DANIEL; MCNEES, ROBERT; SALZER, JAKOB; VALCARCEL, CARLOS; VASSILEVICH, DMITRI. Menagerie of AdS(2) boundary conditions. Journal of High Energy Physics, v. N/A, n. 10, p. 42-pg., . (16/03319-6)
FONTANA, W. B.; BALDIOTTI, M. C.; FRESNEDA, R.; MOLINA, C.. Extended quasilocal Thermodynamics of Schwarzchild-anti de Sitter black holes. ANNALS OF PHYSICS, v. 411, . (15/24380-2, 16/03319-6)
BAGROV, V. G.; GITMAN, D. M.; SHISHMAREV, A. A.; FARIAS JR, A. J. D.. Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems. JOURNAL OF SYNCHROTRON RADIATION, v. 27, n. 4, p. 902-911, . (16/03319-6)
GAVRILOV, S. P.; GITMAN, D. M.. Vacuum instability in slowly varying electric fields. Physical Review D, v. 95, n. 7, . (16/03319-6)
KHUSNUTDINOV, NAIL; EMELIANOVA, NATALIA. The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene. UNIVERSE, v. 7, n. 3, . (19/10719-9, 16/03319-6)
SHISHMAREV, A. A.; LEVIN, A. D.; BAGROV, V. G.; GITMAN, D. M.. Semiclassical Description of Undulator Radiation. JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS, v. 132, n. 2, p. 247-256, . (16/03319-6)
VALCARCEL, CARLOS; VASSILEVICH, DMITRI. Target space diffeomorphisms in Poisson sigma models and asymptotic symmetries in 2D dilaton gravities. PHYSICAL REVIEW D, v. 105, n. 10, p. 10-pg., . (16/03319-6)
ADORNO, T. C.; GITMAN, D. M.; SHABAD, A. E.. Magnetic Pole as Produced by a Point-like Electric Charge Embedded in Constant-Field Background. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, v. 309, n. 1, p. 1-11, . (16/03319-6)
GAVRILOV, S. P.; GITMAN, D. M.; SHISHMAREV, A. A.. Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential. Physical Review D, v. 99, n. 11, . (16/03319-6, 17/05734-3)
KHODAEE, SADI; VASSILEVICH, DMITRI. Note on correlation functions in conformal quantum mechanics. MODERN PHYSICS LETTERS A, v. 32, n. 29, . (16/03319-6)
VASSILEVICH, DMITRI. Index theorems and domain walls. Journal of High Energy Physics, n. 7, . (17/50294-1, 16/03319-6)
GITMAN, D. M.; MEIRELES, M. S.; LEVIN, A. D.; SHISHMAREV, A. A.; CASTRO, R. A.. Entanglement in composite systems due to external influences. International Journal of Modern Physics A, v. 33, n. 21, . (16/03319-6)
FRESNEDA, RODRIGO; GAZEAU, JEAN PIERRE; NOGUERA, DIEGO. Quantum localisation on the circle. Journal of Mathematical Physics, v. 59, n. 5, . (16/03319-6)
MARKOV, YU. A.; MARKOVA, M. A.; GITMAN, D. M.; BONDARENKO, A. I.. PARASTATISTICS AND UNIQUANTIZATION. Russian Physics Journal, v. 61, n. 10, p. 1806-1818, . (16/03319-6)
ANTEZZA, MAURO; FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL. Casimir-Polder force and torque for anisotropic molecules close to conducting planes and their effect on CO2. Physical Review B, v. 102, n. 19, . (16/03319-6, 19/10719-9)
ALMEIDA, CAIO; ALONSO-IZQUIERDO, ALBERTO; FRESNEDA, RODRIGO; MATEOS GUILARTE, JUAN; VASSILEVICH, DMITRI. Nontopological fractional fermion number in the Jackiw-Rossi model. Physical Review D, v. 103, n. 12, . (16/03319-6, 17/50294-1)
GRUMILLER, DANIEL; MCNEES, ROBERT; SALZER, JAKOB; VALCARCEL, CARLOS; VASSILEVICH, DMITRI. Menagerie of AdS(2) boundary conditions. Journal of High Energy Physics, n. 10, . (16/03319-6)
RODRIGUEZ-LOPEZ, PABLO; POPESCU, ADRIAN; FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; WOODS, LILIA M.. Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals. COMMUNICATIONS MATERIALS, v. 1, n. 1, . (19/10719-9, 17/50294-1, 16/03319-6)
IVANOV, V, A.; VASSILEVICH, D. V.. Atiyah-Patodi-Singer index theorem for domain walls. Journal of Physics A-Mathematical and Theoretical, v. 53, n. 30, . (16/03319-6)
KHUSNUTDINOV, N.; WOODS, L. M.. Casimir Effects in 2D Dirac Materials (Scientific Summary). JETP LETTERS, v. 110, n. 3, p. 183-192, . (19/10719-9, 17/50294-1, 16/03319-6)
ADORNO, T. C.; GITMAN, D. M.; SHABAD, A. E.. Magnetic response from constant backgrounds to Coulomb sources. EUROPEAN PHYSICAL JOURNAL C, v. 80, n. 4, . (16/03319-6)
KURKOV, MAXIM; VASSILEVICH, DMITRI. How Many Surface Modes Does One See on the Boundary of a Dirac Material?. Physical Review Letters, v. 124, n. 17, . (17/50294-1, 16/03319-6)
CARDENAS, MARCELA; FUENTEALBA, OSCAR; GONZALEZ, HERNAN A.; GRUMILLER, DANIEL; VALCARCEL, CARLOS; VASSILEVICH, DMITRI. Boundary theories for dilaton supergravity in 2D. Journal of High Energy Physics, v. N/A, n. 11, p. 39-pg., . (16/03319-6)
FIALKOVSKY, I.; KURKOV, M.; VASSILEVICH, D.. Quantum Dirac fermions in a half-space and their interaction with an electromagnetic field. PHYSICAL REVIEW D, v. 100, n. 4, p. 13-pg., . (17/50294-1, 16/03319-6)
RAIMUNDO, K.; BALDIOTTI, M. C.; FRESNEDA, R.; MOLINA, C.. Classical-quantum correspondence for two-level pseudo-Hermitian systems. HYSICAL REVIEW, v. 103, n. 2, p. 13-pg., . (16/03319-6)
FRESNEDA, RODRIGO; GAZEAU, JEAN PIERRE; NOGUERA, DIEGO; KIELANOWSKI, P; ODZIJEWICZ, A; PREVIATO, E. E(2) -covariant integral quantization of the motion on the circle and its classical limit. GEOMETRIC METHODS IN PHYSICS XXXVII, v. N/A, p. 7-pg., . (16/03319-6)
GAVRILOV, S. P.; GITMAN, D. M.; SHISHMAREV, A. A.. Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential. PHYSICAL REVIEW D, v. 99, n. 11, p. 14-pg., . (17/05734-3, 16/03319-6)
ANTEZZA, MAURO; FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL. Casimir-Polder force and torque for anisotropic molecules close to conducting planes and their effect on CO2. PHYSICAL REVIEW B, v. 102, n. 19, p. 11-pg., . (19/10719-9, 16/03319-6)
VASSILEVICH, DMITRI. On the (im)possibility of Casimir repulsion between Chern-Simons surfaces. MODERN PHYSICS LETTERS A, v. 35, n. 3, p. 8-pg., . (16/03319-6)
AFSHAR, HAMID; GONZALEZ, HERNAN A.; GRUMILLER, DANIEL; VASSILEVICH, DMITRI. Flat space holography and the complex Sachdev-Ye-Kitaev model. PHYSICAL REVIEW D, v. 101, n. 8, p. 8-pg., . (16/03319-6)
KURKOV, M.; VASSILEVICH, D.. Parity anomaly in four dimensions. PHYSICAL REVIEW D, v. 96, n. 2, p. 7-pg., . (15/05120-0, 16/03319-6)

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