Related papers: A geometrical interpretation of classical W-transf…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
Working with well known models in $(2+1)D$ we discuss the physics behind the deformation of the canonical structure of these theories. A new deformation is constructed linking the massless scalar field theory with the self-dual theory. This…
Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal…
An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model…
De Broglie waves may be a reflection of a deformation inherent in the path algebra of phase space. On a Riemannian manifold equipped with a suitable 2-form, the product of paths, which is ordinarily their concatenation, can be deformed by…
We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to…
We give a complete equisingular deformation classification of simple spatial quartic surfaces which are in fact $K3$-surfaces.
Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
We discuss the physical consequences of making general phase space deformations on the minisuperspace of phantom cosmology. Based on the principle of physically equivalent descriptions in the deformed theory, we investigate for what values…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
We are studying the dynamics of a one-dimensional field in a non-commutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation…
We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…
This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We…