Related papers: Frame Transformations for Fermions
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
It was shown that in the small Wigner group there is a one-parameter subgroup of the Lorentz transformations, which leave unchanged not only the momentum of the fermion with spin h/2, but also its spin characteristics. This is the group of…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
Models for polarization drag - mechanical analog of the Faraday effect - are extended to include inertial corrections to the dielectrics properties of the rotating medium in its rest-frame. Instead of the Coriolis-Faraday term originally…
The phenomenon of the finite-temperature induced quantum numbers in fermionic systems with topological defects is analyzed. We consider an ideal gas of twodimensional relativistic massive electrons in the background of a defect in the form…
A new approach has been used to evaluate the momentum and angular momentum of the isotropic and homogeneous cosmological models. It is shown that the results obtained for momentum exactly coincide with those already available in the…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
Recently the spectacular result was derived quantum mechanically that the total angular momentum of photons in light beams with finite lateral extensions can have half-integer quantum numbers. In a circularly polarized Gauss light beam it…
Fractional edge states can be viewed as integer edge states of composite fermions. We exploit this to discuss the conductance of the fractional quantized Hall states and the velocity of edge magnetoplasmons.
We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally…
An effective field approximation, similar to the atomic Thomas-Fermi approach, is proposed for studying non-Abelian gauge theories which includes finite-volume effects. As applications of the formalism the equation of state for an SU(2)…
A recently developed energy-dependent frame transformation theory that incorporates both ionization and dissociation channels of the H$_2$ molecule, is extended to treat the ungerade states that occur both in dissociative recombination and…
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…
An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre…
We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a…
We revisit the dynamical equivalence between different representations of vacuum modified gravity models in view of Legendre transformations. The equivalence is discussed for both bulk and boundary space, by including in our analysis the…
We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…
There are confusions about angular momentum propagation in scattering or decay processes involving the transition between particle systems that appear to transform differently under Lorentz transformations. This paper provides an analysis…
We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of…