S. Hacyan

Null geodesic surfaces and Goldberg–Sachs theorem in complex Riemannian spaces

An extension of the Goldberg–Sachs theorem for the case of a complex V4 is given with a simple proof. The interpretation of the theorem, however, no longer applies the concept of the geodesic and shearless congruence of null directions; instead, the existence of a geodesic 2‐surface (complex), the tangent vectorial space to which (i) contains only null vectors, (ii) is parallelly propagated along the surface, is now essential.

Quantum-mechanical properties of Bessel beams

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. As we show explicitly, the operators that are usually associated with linear momentum, orbital angular momentum, and spin do not satisfy the algebra of the translation and rotation group. Nevertheless, we identify some components of these operators that represent observable quantities in an appropriate basis, thus characterizing the quantum numbers of Bessel photons. Some physical consequences of these results are discussed.

Some exceptional electrovac type D metrics with cosmological constant

We investigate all type D solutions of the Einstein–Maxwell equations (with cosmological constant) such that the Debever–Penrose vectors are aligned along the two eigenvectors of the electromagnetic field, in the special case when a direct generalization of the Goldberg–Sachs theorem is not possible. A solution is found which admits no Killing vectors. We also present an extension of the Golberg–Sachs theorem valid for type D metrics.

Some basic properties of Killing spinors

The concept of Killing spinor is analyzed in a general way by using the spinorial formalism. It is shown, among other things, that higher derivatives of Killing spinors can be expressed in terms of lower order derivatives. Conformal Killing vectors are studied in some detail in the light of spinorial analysis: Classical results are formulated in terms of spinors. A theorem on Lie derivatives of Debever–Penrose vectors is proved, and it is shown that conformal motion in vacuum with zero cosmological constant must be homothetic, unless the conformal tensor vanishes or is of type N. Our results are valid for either real or complex space–time manifolds.

Coherent states with elliptical polarization

Coherent states of the two-dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a well-defined elliptical polarization. They are coherent correlated states with respect to the usual Cartesian position and momentum operators. A set of creation and annihilation operators is defined in polar coordinates, and it is shown that these same states are precisely coherent states with respect to such operators.

D (1,0) Killing structures and E potentials

Type D metrics in vacuum or with a special electromagnetic field are studied using the fact that they admit a D (1,0) Killing spinor. It is shown that the E and Φ potentials of Ernst can be obtained in a straightforward way for these types of metrics.

The energy-density spectrum of vacuum in prismatic cavities

Abstract We calculate the explicit form of the energy-density spectrum of scalar vacuum as seen by an observer either at rest or uniformly accelerating, inside a prismatic cavity.

Some type III solutions of the Einstein-Maxwell equations

A Petrov type III metric with nontwisting, degenerate Debever-Penrose direction is studied. This metric is, in general, a solution of the Einstein-Maxwell equations. Two particular cases are investigated in some detail. It is shown that the metric contains typeN, conformally flat and flat metrics as special subcases. Among these subcases, we find the metric of plane gravitational waves and the Bertotti-Robinson solution.

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.

Energy and stress of the Dirac vacuum in a magnetic field

Abstract We calculate the energy and anisotropic pressures exhibited by the Dirac vacuum in the presence of an external uniform magnetic field. We point out that the physical situation bears a certain analogy with the Casimir effect in a cylinder.