Publications

 

Monographs

– Hamiltonian mechanics of gauge systems, Cambridge Monographs on Mathematical Physics,
Cambridge University Press, Cambridge, 2011; 480 pages, ISBN 9780521895125
[with L. V. Prokhorov].
– Hamiltonian dynamics of systems with a gauge symmetry,
JINR Publishing Department, B1-2-93-312, Dubna, 1993; 327 pages (in Russian)
First Edition: St.-Petersburg University Press, St.-Petersburg, 1997; 292 pages (in Russian)
Second Edition: URSS Press, Moscow, 2006; 292 pages (in Russian)
[with L. V. Prokhorov]

Textbooks

Concepts in Calculus III. Multivariable calculus, University Press of Florida, Gainesville, USA, 2012; 650 pages
 Concepts in Calculus II, University Press of Florida, Gainesville, USA, 2012; 250 pages
[with M. Bona]
Concepts in Calculus I, University Press of Florida, Gainesville, USA, 2011; 180 pages
[with M. Bona]

Lecture Notes and Chapters in Books

– Introduction to Partial Differential Equations, Lecture Notes for the course MAP 4341/5345 (University of Florida), 2015; 203 pp
– A brief introduction in the path integral formalism, Valencia university preprint, FTUV-9 6-18, IFIC-96-20, Burjassot, 1996; 106 pages;
– Lectures on quantization of gauge theories by the path integral method, in: Proceedings of the 4th Hellenic school on high energy physics, National Technical University of Athens, Vol. 2, pp. 272 -305 (Ed. E.N. Gazis, G. Koutsoumbas, N.D. Tracas, and G. Zoupanos) , Athens, 1994 (in Corfu 1992; Elementary Particle Physics, Vol. 1; pp 272 – 356)
– The gauge invariance, toroid order parameters and radiation in electromagnetic theory,
in: Essays on Formal Aspects of Electromagnetic Theory (ed. by A.Lakhtakia), World Scientific, New Jersey, 1993, pp. 399-474
[with V. M. Dubovik]
– Phase space structure in gauge theories, JINR series “Lectures for Young Scientists”, P2-89-533, JINR, Dubna, 1989; 84 pages

Invited Review Papers

– Resonant light scattering and higher harmonic generation by periodic subwavelength arrays,
Int. J. Mod. Phys. B 23 (2009) 5191-5239
– Geometry of the physical phase space in quantum gauge systems,
Physics Reports 326 (2000) 1 – 163
– 2D Yang-Mills theories, gauge orbit spaces and the path integral quantization,
Commun. Theor. Phys. 4 (1995) 1 – 38
– Phase space structure in mechanical models with a gauge group,
Sov. Phys. Uspekhi, 34(2) (1991) 108-140
[with L. V. Prokhorov]

Papers

– Bound states in the continuum in elasticity,
Wave Motion (2021) 103: 102718
[with O.Haq]
– Concurrent atomistic-continuum modeling of crystalline materials,
Journal of Applied Physics (2019) 126: 101101
[with Y. Cheng and D.L. McDowell]
– Equilibrium chemistry in BCl_3H_2Ar plasma,
Plasma Chem. and Plasma Proc. (2019) 39: 1087-1102
[with I.B. Gornushkin and P.G. Sennikov]
– Error analysis in optimization problems relevant for calibration-free laser-induced breakdown spectroscopy,
J. Quant. Spectrosc. Rad. Trans. (2019) 222-223: 236-246
[with J.J. Maali]
– Chemistry in laser-induced plasmas at local thermodynamic equilibrium
Appl. Phys. A (2018) 124: 716
[with I.B. Gornushkin]
– Geometrical effects in data collection and processing for  calibration-free laser-induced breakdown spectroscopy ,
J. Quant. Spectrosc. Rad. Trans. (2018) 204: 190-205
[with I.B. Gornushkin]
– Anions in laser-induced plasmas,
Appl. Phys. A (2016) 122: 676
[with I.B. Gornushkin]
– Modeling chemical reactions in laser-induced plasmas,
Appl. Phys. A (2015) 121:1087–1107
[with I.B. Gornushkin]
-Two-dimensional axisymmetric models of laser induced plasmas relevant to laser induced breakdown spectroscopy,
Spectrochimica Acta Part B: Atomic Spectroscopy, 100 (2014) 147-172
[with I.B. Gornushkin]
– Electromagnetic Siegert states for periodic dielectric structures,
J. Math. Phys. (submitted)
[with R. F. Ndangali]
– The resonant nonlinear scattering theory with bound states in the radiation continuum and the second harmonic generation ,
Proc. SPIE 8808, Active Photonic Materials V, 88081F (September 11, 2013), 18 pages, DOI:10.1117/12.2028277;
[with R. F. Ndangali]
– Tomography of Single and Double Pulse laser induced plasma using the Radon transform,
J. Anal. Atom. Spectr., Spectrochim. Acta Part B: Atom. Spectr. (2012), DOI information: 10.1016/j.sab.2012.06.033
[with I.B. Gornushkin, S. Merk, A. Demidov, U. Panne, B.W. Smith, and N. Omenetto]
– Absorption tomography of laser induced plasmas,
J. Quan. Spectr. Rad. Trans. 113 (2012) 518-523.
[with I.B. Gornushkin]
– Laser-induced plasma tomography by the Radon transform,
J. Anal. Atom. Spectr. 26 (2011) 2483-2492.
[with I.B. Gornushkin, S. Merk, and U. Panne]
– Emission plasma tomography with large acceptance angle apertures relevant to laser induced plasma spectroscopy,
Spectrochimica Acta Part B: Atomic Spectroscopy, 66 (2011) 413-420
[with I.B. Gornushkin]
– Abel inversion applied to a transient laser induced plasma: implications from plasma modeling,
J. Anal. At. Spectrom., 26 (2011) 1457-1465
[with I.B. Gornushkin and U. Panne]
– Electromagnetic bound states in the radiation continuum for periodic double arrays of subwave-
length dielectric cylinders
,
J. Math. Phys. 51 (2010) 102901
[with R. F. Ndangali]
– Effects of non-uniformity of laser induced plasma on plasma temperature and concentrations
determined by the Boltzmann plot method: Implications from plasma modeling
,
J. Anal. Atom. Spectr. 25 (2010) 1643-1653
[with I. B. Gornushkin, S. Merk, E. Tognoni, and U. Panne]
– The flip-over effect in self-similar laser-induced plasma expansion,
J. Math. Phys. 49, 093101 (2008)
[with N P Baxter]
– Bound States in the Continuum in Photonics,
Phys. Rev. Lett. 100, 183902 (2008)
[with A. G. Borisov and D. C. Marinica]
– Radiation from asymmetric laser-induced plasmas collected by a lense or optical fiber,
Appl. Optics, 47, 1745 (2008)
[with I. B. Gornushkin and J. D. Winefordner]
– Second harmonic generation from arrays of subwavelength cylinders,
Phys. Rev. B 76, 085311 (2007)
[with D. C. Marinica and A. G. Borisov]
– Trapped electromagnetic modes and scaling in the transmittance of perforated metal films,
Phys. Rev. Lett. 97 (2006) 67403
[with S. Selcuk, K. Woo, D. B. Tanner, A. F. Hebard, and A. G. Borisov]
– Non-isothermal asymmetric expansion of laser induced plasmas into vacuum,
J. Appl. Phys. 100 (2006) 073304
[with I. B. Gornushkin, N. Omenetto, and J. D. Winefordner]
– Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive
media
,
J. Comput. Phys. 216 (2006) 391-402
[with A. G. Borisov]
– Tunneling mechanism of light transmission through metallic films,
Phys. Rev. Lett. 95 (2005) 067403-1
[with F.G. Garcia de Abajo, G. Gomeez-Santos, L.A. Blanco, and A.G. Borisov]
– Role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials,
Phys. Rev. B 71 (2005) 075408
[with A. G. Borisov and F.J. Garcia de Abajo]
– Lanczos Pseudospectral Method for Initial-Value Problems in Electrodynamics and its Applica-
tions to Ionic Crystal Grating
,
J. Comput. Phys. 209 (2005) 643-664
[with A. G. Borisov]
– Applications of the wave packet method to resonant transmission and reflection gratings,
J. Comput. Phys. 199 (2004) 742-762
[with A. G. Borisov]
– An application of interpolating scaling functions to wave packet propagation,
Comput. Phys. Commun. 160 (2004) 1-7
[with A. G. Borisov]
– The wave packet propagation using wavelets,
Chem. Phys. Lett. 361 (2002) 15-20
[with A. G. Borisov]
– On a low energy bound in a class of chiral field theories with solitons,
J. Math. Phys. 43 (2002) 4127-4134
– Infrared Yang-Mills theory as a spin system. A lattice approach,
Phys. Lett. B 522 (2001) 201-209
– Charge transfer interaction in the F- -Cu(111) and -Ag(111) systems: Treatment of the fluorine
quasi-equivalent electrons
,
Surf. Sci. 487 (2001) 243-257
[with A. G. Borisov and J. P. Gauyacq]
– Yang-Mills theory as an Abelian theory without gauge fixing,
Phys. Lett. B 463 (1999) 263-272
– An effective action for monopoles and knot solitons in Yang-Mills theory,
Phys. Lett. B 458 (1999) 322-330
– The inverse variational problem for autoparallels,
J.Phys.A: Math.Gen. 32 (1999) 5355-5366
[with C. Maulbetsch]
– Towards a nonperturbative path integral in gauge theories,
Phys. Lett. B 456 (1999) 38-47
[with J. R. Klauder]
– BRST inner product spaces and the Gribov obstruction,
Nucl. Phys. B 538 (1998) 485-514
[with N. Duechtig and T. Strobl]
– Path Integral Quantization and Riemannian-Symplectic Manifolds,
Phys. Lett. B 435 (1998) 343-349
[with J. R. Klauder]
– Constrained Systems and Analytical Mechanics in Spaces with Torsion,
J. Phys. A: Math. Gen. 31 (1998) 5177 – 5190
– Brownian Motion of Massive Particle in a Space with Curvature and Torsion and Crystals with
Defects
,
J. Phys. A: Math. Gen. 31 (1998) 7005-7009
[with H. Kleinert]
– Spaces with Torsion from Embedding and the Special Role of Autoparallel Trajectories,
Phys. Lett. B 428 (1998) 315-321
[with H. Kleinert]
– Coordinate-Free Quantization of Second-Class Constraints,
Nucl. Phys. B 511 (1998) 713-736
[with J. R. Klauder]
– Gribov vs BRST,
Ann. Phys. (NY), 263 (1998) 119-132
[with F. G. Scholtz]
– Supersymmetry in Stochastic Processes with Higher Order Time Derivatives,
Phys. Lett. A 235 (1997) 105-112
[with H. Kleinert]
– Proper Dirac Quantization of Free Particle on D-dimensional Sphere,
Phys. Lett. A 232 (1997) 327-332
[with H. Kleinert]
– Coordinate-free quantization of first-class constrained systems,
Phys. Lett. B 398 (1997) 116
[with J. R. Klauder]
– Dynamical Abelian projection of gluodynamics,
Nucl. Phys. Proc. Suppl. 54A (1997) 213-216
– Abelian projection and numerical studies of gauge-variant quantities in lattice QCD without
gauge fixing
,
Mod. Phys. Lett. A 11 (1996) 1081-1093
– Quantum Langevin equation from forward-backward path integral,
Phys. Lett. A 200 (1995) 224-232
[with H. Kleinert]
– q-oscillators, (non-)Kaehler manifolds and constrained dynamics,
Mod. Phys. Lett. A 10 (1995) 941-948
– String-like excitations in quantum electrodynamics,
Theor. Math. Phys. (USSR), 97 (1993) 1323-1423
[with L. V. Prokhorov and D. V. Fursaev]
– Phase space structure and the path integral for gauge theories on a cylinder,
Phys. Lett. B 318 (1993) 323-330
– Quantum and classical dynamics of q-deformed systems,
J. Phys. A: Math. Gen. 26 (1993) 2583-2606
– The Poisson bracket for q-deformed systems,
J.Phys. A: Math.Gen. 25 (1992) L1245-L1250
– Path integral for the q-deformed oscillator and its interpretation,
Phys. Lett. B 293 (1992) 117-122
– String-like excitations in QED,
Mod. Phys. Lett. A 7 (1992) 3441-3447
[with D. V. Fursaev and L. V. Prokhorov]
– Invariant structures in gauge theories and confinement,
Int. J. Mod. Phys. A 7 (1992) 7815-7840,
[with L V Prokhorov]
– Non-perturbative Green functions in quantum gauge theories,
Mod. Phys. Lett. A 6 (1991) 909-921
– The phase space structure in minisuperspace cosmological models,
Phys. Lett. B 272 (1991) 11-16
– Quantization of constrained systems and path integral in curvilinear supercoordinates,
J. Phys. A: Math. Gen. 24 (1991) 1199-1214
– Phase space reduction and the choice of physical variables in gauge theories,
Int. J. Mod. Phys. A 6 (1991) 845-863
– Path integral for the Yang-Mills theory in a non-perturbative region,
Phys. Lett. B 255 (1991) 398-404
– Transverse-longitudinal part of the vector potential in classical electrodynamics,
J. Phys. A: Math. Gen. 23 (1990) 3245-3255; Erratum: ibid. A 24 (1991) 523
[with V. M. Dubovik]
– Pecularities of the dynamics of fermi-systems with a gauge group (on the nature of the Higgs field),
Vestnik LGU, ser.4, 4 (1990) 3-7
[with L. V. Prokhorov]
– On quantum mechanics of systems with a gauge group,
Theor. Math. Phys. (USSR) 78 (1989) 292-312
– Free-field potentials in electrodynamics,
Phys. Lett. A 142 (1989) 211-214
[with V. M. Dubovik]
– The role of the Weyl group in gauge theories,
Phys. Lett. B 216 (1989) 341-344
[with L .V. Prokhorov
– Path integral for quantum mechanical systems with an arbitrary gauge group,
Vestnik LGU, ser.4, 11 (1988) 8-14 (in Russian)
[with L. V. Prokhorov]
– Hamiltonian path integral for systems with conic phase space,
Vestnik LGU, ser.4, 4 (1988) 68-71 (in Russian)
[with L. V. Prokhorov]
– Dynamical systems with a gauge group,
VINITI, 7961-B87, Leningrad, 1987 (in Russian) (57 pp)
[with L. V. Prokhorov]
– On vortex rings,
Kvant, issue 11, (1979) 17-21
[with V. Shubin]

 

Proceedings of Conferences (16)

– On an effective action of monopoles in Abelian projections of Yang-Mills theories,
in: 11th Rencontres de Blois: Frontiers of Matter, Ed. Tran Thanh Van, Jean (The Gioi Publishers, Vietnam, 2001), p. 315-320; on-line LANL electronic archive: hep-th/0004135 (The proceedings of the conference “Frontiers of Matter”, June 1999, Blois, France)
– An Introduction to Coordinate-free Quantization and its Application to Constrained Systems,
in: Mathematical Methods of Quantum Physics, Eds. C C Bernido et al, (Gordon and Breach Science Publishers, Amsterdam, 1999), pp. 117-130. (The proceedings of a workshop, Janga, Bohol, Philippines, January, 1998)
[with J. R. Klauder]
– Path integral in holomorphic representation without gauge fixation,
in: The Proceedings of “Path Integrals 96”, (ed. by V S Yarunin and M A Smondyrev) JINR, Dubna, 1996, p. 133-138 (JINR preprint, E2-89-687); on-line LANL electronic archive: quant-ph/9608018.
– Confinement in 3D gluodynamics as a 2D critical phenomenon,
in: The Proceedings of “Quark Confinement”, Como, Italy, June, 1996 (World Scientific, Singapore, 1997); p. 242-245; on-line LANL electronic archive: hep-th/9701006
[with A. Ferrando and A. Jaramillo]
– SUSY quantization of gauge theories and applications,
in: The Proceedings of 2nd Sakharov Conference on Physics, Moscow, May, 1996, ed. I M Dremin and A M Semikhatov (World Scientific, Singapore, 1997); p. 558-561; on-line LANL electronic archive: hep-th/9606074
[with F. G. Scholtz]
– Dirac potentials in gauge models,
in: Group Theoretical Methods in Physics (Yamada conference on Mathemathical Physics, Kyoto, Japan), ed. by A Arima et al, World Scientific, Singapore, 1995, p.423-427
– A transition amplitude on the gauge orbit space,
in: Constraint Theory and Quantization Methods (Montepulciano, Italy), ed. by F Colomo et al, World Scientific, Singapore, 1994, p.176-189
– On minisuperspace gauge models with fermions,
in: Proceedings of the first Iberian meeting on classical and quantum gravity (Evora, Portugal), ed. M. C. Bento et al, World Scientific, Singapore, 1993, p.322-331
– Q-deformed systems and constrained dynamics
in: Proceedings of XXVIth International Symposium on elementary physics (Wendisch-Rietz, Germany), ed. B. Doerfel, DESY 93/13, 1993, p.276-286
– Gauge field invariants and confinement,
Proceedings of the 1st Sakharov conference on Physics, ed. by L V Keldysh and V. Ya. Fainberg, Nova Science Publishers, 1992, Vol. 1, p.141-149
[with L. V. Prokhorov]
– Phase space structure in gauge theories and quantum dynamics,
in: The Proceedings of the II International Wigner Symposium (15-20 July, 1991, Goslar, Germany), p.698-702
– Green functions in collective variables for systems with a gauge group,
in: The Proceedings of the XIII Seminar on High Energy Physics and Field Theory, Nauka, Moscow, 1991 (IHEP, Protvino, 9-13 July, 1990) p.127-131
– Path integral without gauge fixing in coordinate representation,
in: Theory of Representations and Group Methods in Physics , Moscow , Nauka, 1991 (in Russian)
– A vector potential in electrodynamics,
in: Theory of Representations and Group Methods in Physics , Moscow , Nauka, 1991 (in Russian)
[with V. M. Dubovik]
– Path integral in collective variables for Yang-Mills theory,
in: Symmetries and algebraic structures in physics, Vol. 1, p. 125-130, Moscow, 1990,
– Phase space structure of gauge theories and quasiclassical description,
in: Topological Phases in Quantum Theory, pp.354-370, Singapore, WSPC, 1989
[with L. V. Prokhorov]

Preprints and Technical Reports (14)

– Applications of the Slepian functions on the sphere to numerical modeling of narrow
beam electromagnetic pulses
,
Technical Report for Contract UPN-05040506, June, 2005; 41 pp (classified by the US Air Force and SAIC corporation)
– Lanczos Pseudospectral Propagation Method for Initial-Value Problems in Electrodynamics of
Passive Media
,
on-line LANL electronic archive: physics/0410271, 2004
[with A. G. Borisov]
– Electromagnetic Pulse Propagation in Passive Media by the Lanczos Method,
on-line LANL electronic archive: physics/0410270, 2004
[with A. G. Borisov]
– Electromagnetic pulse propagation in passive media by path integral methods,
on-line LANL electronic archive: math.NA/0312296, 2003
– Applications of the filter diagonalization technique to SAR signal processing,
Technical Report for a US Air Force research project, US Air Force Grant F4920-03-1-0414; September, 2003 (sent to the Air Force Research Laboratory, Brooks, San-Antonio, TX)
– Image analysis using polarization properties of electromagnetic waves,
Technical Report for a US Air Force research project, US Air Force Grants F4920-03-1-0414 and F49620-01-1-0473; February, 2003 (sent to the Air Force Research Laboratory, Brooks,
San-Antonio, TX)
– A path integral approach to electromagnetic pulse propagation in dispersive media,
Technical Report for a US Air Force research project, US Air Force Grant F4920-03-1-0414; December, 2002 (sent to the Brooks Air Force Base, San-Antonio, TX)
– The monopole dominance in QCD,
Valencia University preprint, IFIC-96-70, FTUV-96-62, Burjassot, 1996; on-line LANL electronic archive: hep-th/9611228.
– Supersymmetric quantization of gauge theories,
Valencia University preprint, IFIC-96-66, FTUV-96-58, Burjassot, 1996; on-line LANL electronic archive: hep-th/9509015
[with F Scholtz]
– On a possible solution of the Gribov problem,
CEA Saclay preprint, T 94/045, CEA, Saclay, 1994.
– The proper field of charges and gauge-invariant variables in electrodynamics,
JINR preprint, E2-92-136, JINR, Dubna, 1992.
– Invariant structures and static forces in gauge theories,
JINR preprint, E2-91-266, JINR, Dubna, 1991
[with L. V. Prokhorov]
– Phase space structure of the Yang-Mills fields,
JINR preprint, E2-90-207, JINR, Dubna, 1990
[with L. V. Prokhorov]
– The role of gauge invariants in path integral construction,
JINR preprint, E2-89-688, JINR, Dubna, 1989