Related papers: Relativistic partial waves for celestial amplitude…
Selection of physically meaningful solutions of the Wheeler-DeWitt equation for the wavefunction in quantum cosmology, can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical…
In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space $\Omega =\mathbb R^3_+$ given by the self-adjoint operator named $\delta$-interaction. We will assume Dirichlet or Neumann boundary…
We show that the fractional Laplacian can be viewed as a Dirichlet-to-Neumann map for a degenerate hyperbolic problem, namely, the wave equation with an additional diffusion term that blows up at time zero. A solution to this wave extension…
The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, by using the so called adiabatically-amplified zero-point fluctuations process, it has been shown how the…
The extremely high precision of current astronomical observations demands a much better theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of isolated…
We investigate the dynamical Casimir effect for a one-dimensional resonant cavity, with one oscillating mirror. Specifically, we study the discrete spectrum of created particles in a region of frequencies above the oscillation frequency…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
The all-loop resummation of SU$(N)$ gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a…
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to…
The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a…
A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first…
The cosmological stochastic gravitational-wave background produced by the mildly non-linear evolution of density fluctuations is analyzed, in the frame of an Einstein-de Sitter model, by means of a fully relativistic perturbation expansion…
We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the…
I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of…
We study an intrinsic distribution, called polar, on the space of $l$-dimensional integral elements of the higher order contact structure on jet spaces. The main result establishes that this exterior differential system is the prolongation…
Approximate bound state solutions of the Dirac equation with the Hulth\'en plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave…
The geometric optics approximation traditionally used to study the propagation of gravitational waves on a curved background, breaks down in the vicinity of compact and extended astrophysical objects, where wave-like effects like diffusion…
We derive exact series solutions for the Wheeler-DeWitt equation corresponding to a spatially closed Friedmann-Robertson-Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The…