Related papers: Frame Transformations for Fermions
The alternative to the standard formulation of QPM in the infinite momentum frame is suggested. The proposed approach does not require any extra assumptions in addition, consistently takes into account the parton transversal momenta and…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schr\"odinger…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
The influence of spatial geometry on the vacuum polarization in 2+1-dimensional spinor electrodynamics is investigated. The vacuum angular momentum induced by an external static magnetic field is found to depend on global geometric surface…
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such…
In the Light-Front Dynamics, the wave function equations and their numerical solutions, for two fermion bound systems, are presented. Analytical expressions for the ladder one-boson exchange interaction kernels corresponding to scalar,…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
This article discusses the construction of dual frames and their uniqueness for the multiplication generated frames on $L^2(X; \mathcal H)$, where $X$ is a $\sigma$-finite measure. A necessary and sufficient condition of such duals…
Fundamental and applied concepts concerning the ability of light beams to carry a certain mechanical angular momentum with respect to the propagation axis are reviewed and discussed. Following issues are included: Historical reference;…
The appearance of angular momentum in the nuclear motion of molecular systems lacking inversion symmetry under imposed thermal gradients presents a novel mechanism with potential implications for spintronics, magnetic response, and energy…
We study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local…
Statistics transmutations to composite fermions in fractional-quantum-Hall-effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground-state energy shows that the transmutations are not…
The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when…
We show theoretically that it is possible to trap and cool the rotational motion of a macroscopic mirror made of a perfectly reflecting spiral phase element using orbital angular momentum transfer from a Laguerre-Gaussian optical field.…
Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether's theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the…
The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of…