Related papers: From Amplitudes to Analytic Wavefunctions
We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a…
In the framework of decay theory of Goldberger and Watson we treat $\alpha$-decay of nuclei as a transition caused by a residual interaction between the initial unperturbed bound state and the scattering states with alpha-particle. The…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
We introduce Wave Arithmetic, a smooth analytical framework in which natural, integer, and rational numbers are represented not as discrete entities, but as integrals of smooth, compactly supported or periodic kernel functions. In this…
Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we…
From the graviton-graviton scattering amplitudes calculated perturbatively in quantum gravity to the one-loop order, we develop further a formalism that allows one to calculate infrared-finite partial-wave amplitudes fulfilling perturbative…
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…
Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been…
In these proceedings, we discuss the recent approach of Ref. [1] for the construction of compact Ans\"atze for scattering amplitudes. The method builds powerful constraints on the analytic structure of the rational functions in amplitudes…
We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. We associate to this space a point-wise notion of quantum…
We show that cosmological wavefunctions in $\phi^n$ theories naturally generalize flat-space $\mathrm{Tr}(\phi^3)$ scattering amplitudes: via a simple map from tube variables to Mandelstam invariants, each wavefunction coefficient…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…
We specify the semiclassical no-boundary wave function of the universe without relying on a functional integral of any kind. The wave function is given as a sum of specific saddle points of the dynamical theory that satisfy conditions of…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at…
Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity…
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering…
We review completely monotone (CM) and Stieltjes functions, which are classes of functions obeying an infinite hierarchy of positivity constraints. While these are classical concepts in analysis, such properties have recently been shown to…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…