Related papers: From Amplitudes to Analytic Wavefunctions
The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic…
The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions…
A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude…
Flat-space physics is highly constrained by basic principles such as Lorentz invariance, locality, unitarity and causality. This is neatly seen in the structure of scattering amplitudes. For processes occurring in an expanding background we…
We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the…
The physical information encoded in the cosmological late-time wavefunction of the universe is tied to its singularity structure and its behaviour as such singularities are approached. One important singularity is identified by the…
We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link…
Cosmological observables of the primordial universe are encoded in the late-time field-theoretic wavefunction. For shift-symmetric scalars in de Sitter, a good approximation for many inflationary models, the wavefunction must be purely real…
We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless…
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…
This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…
It is shown that `bipartite' wave functions can present a mathematical formalism of quantum theory for a single particle, in which the associated Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions of product…
We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
The theoretical interpretation of measurements of "wavefunctions" and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the…
This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities. The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open…
A general type of localized excitations, folded solitary waves and foldons, are defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich…