Related papers: On the tomographic description of classical fields
Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of…
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…
It is shown that dynamical equations for quantum tomograms retain the normalization conditions of their solutions during evolution only if the solutions satisfy a set of special conditions. These conditions are found explicitly. On the…
The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the tomographic probability representation of quantum mechanics. The states are expressed in terms of quantum tomograms. The coherent…
Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture…
States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl-Wigner-Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
The canonical quantization of the tachyon field is suggested. Quantization is based on the conception of stable and unstable components of the tachyon degrees of freedom.
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
This paper is a follow-up to a previous paper on fermions. A simple state sum model for a scalar field on a triangulated 1-manifold is constructed. The model is independent of the triangulation and gives exactly the same partition function…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…