Related papers: Path and Path Deviation Equations in Kaluza-Klein …
We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al., and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial…
A generation procedure, based on the 5-dimensional covariance of the Kaluza-Klein theory, is developed. The procedure allows one to obtain exact solutions of the 4-dimensional Einstein equations with electromagnetic and scalar fields from…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
We develop a linearized five dimensional Kaluza-Klein theory as a gauge theory. By perturbing the metric around flat and the De Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular…
In theories of the Kaluza-Klein kind there are spins or total angular moments in higher dimensions which manifest as charges in the observable $d=(3+1)$. The charge conjugation requirement, if following the prescription in ($3+1$), would…
We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…
In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…
Electron-plasmon interaction in a thin cylindrical wire is described in terms of four-dimensional Kaluza-Klein theory in which angular coordinate of the metal cylinder is considered to be one of the two compactified coordinates. In this…
In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
We investigate quantum gravity in the path integral formulation using the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
The geometrization of the Electro-Weak Model is achieved in a 5-dimensional Riemann-Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extra-coordinate and of a normalization…
The aim of this paper is to study large deviations for the self-similar solution of a Kac-type kinetic equation. Under the assumption that the initial condition belongs to the domain of normal attraction of a stable law of index $\alpha <2$…
The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orientations. We study the acceleration of spinning particles by an electric field, as well as the…