Related papers: Velocity field and operator in (non relativistic) …
The Bessel operator, that is, the Schr\"odinger operator on the half-line with a potential proportional to $1/x^2$, is analyzed in the momentum representation. Many features of this analysis are parallel to the approach \`a la K. Wilson to…
We present a derivation of a position operator for a massive field with spin $1/2$, expressed in a representation-independent form of the Poincar\'e group. Using the recently derived Lorentz-covariant field spin operator, we obtain a…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…
In the most general geometric background, we study Dirac spinor fields with particular emphasis given to the explicit form of their gauge momentum and the way in which this can be inverted so to give the expression of the corresponding…
A covariant quantization of the free spinor fields (s=1/2) in 4-dimensional de Sitter (dS) space-time based on analyticity in the complexified pseudo-Riemanian manifold is presented. We define the Wigthman two-point function ${\cal…
We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\hbar$. Going beyond leading order in $\hbar$ we then derive a generalized Boltzmann equation…
We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We…
We investigate spin- and velocity-dependent contributions to the gravitational inter-particle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections.…
We give a systematic treatment of a spin 1/2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
Non-relativistic quantum field theory is a framework that describes systems where the velocities are much smaller than the speed of light. A large class of those obey Schr\"{o}dinger invariance, which is the equivalent of the conformal…
A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0…
Quantum Gravity has been so elusive because we have tried to approach it by two paths which can never meet: standard quantum field theory and general relativity. The gateway is covariance under the complexified Clifford algebra of our…
We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady)…
Emerging possibilities for creating and studying novel plasma regimes, e.g. relativistic plasmas and dense systems, in a controlled laboratory environment also requires new modeling tools for such systems. This brings motivation for…
The aim of this work is to show, on the example of the behaviour of the spinless charged particle in the homogeneous electric field, that one can quantized the velocity of particle by the special gauge fixation. The work gives also the some…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…