Sergei V. Shabanov

Tunneling Mechanism of Light Transmission through Metallic Films

A mechanism of light transmission through metallic films is proposed, assisted by tunneling between resonating buried dielectric inclusions. This is illustrated by arrays of Si spheres embedded in Ag. Strong transmission peaks are observed near the Mie resonances of the spheres. The interaction among various planes of spheres and interference effects between these resonances and the surface plasmons of Ag lead to mixing and splitting of the resonances. Transmission is proved to be limited only by absorption. For small spheres, the effective dielectric constant of the resulting material can be tuned to values close to unity, and a method is proposed to turn the resulting materials invisible.

An Effective action for monopoles and knot solitons in Yang-Mills theory

Abstract By comparison with numerical results in the maximal Abelian projection of lattice Yang–Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang–Mills connection is parameterized in a special way to separate the dependence on the coset field. The coset field is then regarded as a collective variable, and a method to obtain its effective action is developed. It is argued that the physical excitations of the effective action may be knot solitons. A procedure to calculate the mass scale of knot solitons is discussed for lattice gauge theories in the maximal Abelian projection. The approach is extended to the SU( N ) Yang–Mills theory. A relation between the large N limit and the monopole dominance is pointed out.

Proper Dirac quantization of a free particle on a D-dimensional sphere

Abstract We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in D dimensions is possible only by converting the constraints to Abelian gauge constraints, which are of first class in Diracs classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Diracs modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.

Geometry of the physical phase space in quantum gauge systems

Abstract The physical phase space in gauge systems is studied. Simple soluble gauge models are considered in detail. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang–Mills type with fermions that takes into account the non-Euclidean geometry of the physical phase space. The new path integral is applied to resolve the Gribov obstruction. Applications to the Kogut–Susskind lattice gauge theory are given. The basic ideas are illustrated with examples accessible for non-specialists.

Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders

Electromagnetic bound states in the radiation continuum are studied for periodic double arrays of subwavelength dielectric cylinders in TM polarization. They are similar to localized waveguide mode solutions of Maxwell’s equations for metal cavities or defects of photonic crystals, but, in contrast to the latter, their spectrum lies in the radiation continuum. The phenomenon is identical to the existence of bound states in the radiation continuum in quantum mechanics, discovered by von Neumann and Wigner. In the formal scattering theory, these states appear as resonances with the vanishing width. For the system studied, the bound states are shown to exist at specific distances between the arrays in the spectral region where one or two diffraction channels are open. Analytic solutions are obtained for all bound states (below the radiation continuum and in it) in the limit of thin cylinders (the cylinder radius is much smaller than the wavelength). The existence of bound states is also established in the sp...

Coordinate-free quantization of first-class constrained systems

Abstract The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.

On a low energy bound in a class of chiral field theories with solitons

A low energy bound for static classical solutions in a class of chiral solitonic field theories related to the infrared physics of the SU(N) Yang–Mills theory is established.

Coordinate-free quantization of second-class constraints

Abstract The conversion of second-class constraints into first-class constraints is used to extend the coordinate-free path-integral quantization, achieved by a flat-space Brownian motion regularization of the coherent-state path-integral measure, to systems with second-class constraints.

Quantum Langevin equation from forward-backward path integral

Abstract The quantum Langevin equation is derived from the Feynman-Vernon forward-backward path integral for a density matrix of a quantum system in a thermal oscillator bath. We exhibit the mechanism by which the classical, c-valued noise in the Feynman-Vernon theory turns into an operator-valued quantum noise. The quantum noise fulfills a characteristic commutation relation which ensures the unitarity of the time evolution in the quantum Langevin equation.

Hamiltonian Mechanics of Gauge Systems

1. Hamiltonian formalism 2. Hamiltonian path integrals 3. Dynamical systems with constraints 4. Quantization of constrained systems 5. Phase space in gauge theories 6. Path integrals in gauge theories 7. Confinement 8. Supplementary material Index.