Related papers: Canonical transformation for stiff matter models i…
The Sommerfeld-Watson transformation is a powerful mathematical technique widely used in physics to simplify summations over discrete quantum numbers by converting them into contour integrals in the complex plane. This method has…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical…
The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different…
In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is well-known, the corresponding Hamiltonian can be…
A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation and a cosmological…
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…
We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which…
We illustrate how the group of symmetry transformations, which preserve the form of the n--dimensional flat Friedmann--Robertson--Walker cosmologies satisfying Einstein equations, acts in any dimension. This group relates the energy density…
A pair of Hermitian operators is canonical if they satisfy the canonical commutation relation. It has been believed that no such canonical pair exists in finite-dimensional Hilbert space. Here, we obtain canonical pairs by noting that the…
We study dynamical systems which admit action-angle variables at leading order which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical…
When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…