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Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…
Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their…
The radiation caused by particles of one bunch in the collective electromagnetic field of the short oncoming bunch is studied. Quantum effects are calculated for the spectrum of radiated photons. Using this spectrum, the dependence of the…
Interplay between the effects of coherent radiation and localization of light is analysed. A system of two-level atoms is placed in a medium interacting with electromagnetic field. The matter-light interaction can result in the appearance…
Field theories compactified on non-simply connected spaces, which in general allow to impose twisted boundary conditions, are found to unexpectedly have a rich phase structure. One of characteristic features of such theories is the…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
We continue studying the properties of $\gamma_0$-compact, $\gamma^*$-regular and $\gamma$-normal spaces defined in [5]. We also define and discuss $\gamma$-locally compact spaces.
We study the radiation of photons from a classical charged particle. We particularly consider a situation where the particle has a constant velocity in the distant past, then is accelerated, and then has a constant velocity in the distant…
We develop a general formalism for treating radiative degrees of freedom near $\mathscr{I}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into…
On the example of stationary states of a system consisting of an atom and a quantized electromagnetic field (the Jaynes-Cummings model in free space), it is shown that the physical characteristics of the system (as the energy and the…
Although the whole conformal group $SO(4,2)$ can be considered as a symmetry in a classical massless field theory, the subgroup of special conformal transformations (SCT), usually related to transitions to uniformly accelerated frames,…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
Radiation by the atoms of a resonant medium is a cooperative process in which the medium participates as a whole. In two previous papers \cite{PG00,GP00}, we treated this problem for the case of a medium having slab geometry, which, under…
We introduce quantum optical dipole radiation fields defined in terms of photon creation and annihilation operators. These fields are identified through their spatial dependence, as the components of the total fields that survive infinitely…
Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light…
The quantization of a scalar field in anti de Sitter spacetime using Poincar\'e coordinates is considered. We find a discrete spectrum that is consistent with a possible mapping between bulk and boundary quantum states.