Related papers: Quantifying momenta through the Fourier transform
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a…
We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian…
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…
We derive exact expressions, in the form of Fourier integrals over the (k,w) domain, for the energy, momentum, and angular momentum of a light pulse propagating in free space. The angular momentum is seen to split naturally into two parts.…
We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.
We calculate momentum imparted by colliding gravitational waves in a closed Friedmann Robertson-Walker background and also by gravitational waves with toroidal wavefronts using an operational procedure. The results obtained for toroidal…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
The solution of a causal fractionary wave equation in an infinite potential well was obtained. First, the so-called "free particle" case was solved, giving as normalizable solutions a superposition of damped oscillations similar to a wave…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
Based on the Caputo fractional derivative the classical, non relativistic Hamiltonian is quantized leading to a fractional Schroedinger type wave equation. The free particle solutions are localized in space. Solutions for the infinite well…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first…
A single electromagnetic plane-wave propagating in free space possesses neither spin nor orbital angular momentum. Both types of angular momentum arise from interference between pairs of plane-waves having the same temporal frequency…
An energy-momentum carried by electromagnetic field produced by two point-like charged particles is calculated. Integration region considered in the evaluation of the bound and emitted quantities produced by all points of world lines up to…
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…