Related papers: Towards a Generalized Distribution Formalism for G…
We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains…
An approach featuring $s$-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle-angular momentum coherent states must be…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under…
Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as…
In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
We extend the construction of generalized Berezin and Berezin-Toeplitz quantization to the case of compact Hodge supermanifolds. Our approach is based on certain super-analogues of Rawnsley's coherent states. As applications, we discuss the…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…
Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of…
We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion…
We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes fit well within the general framework of the weighted matrices approach to ultradifferentiable…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Shilov spaces. Important examples of multiresolution analyses…
The relation of generalized (skewed) quark distributions to nucleon wave functions is discussed in the context of light-cone quantization.
In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential conver- gence towards the quasi-stationary distribution for the generalized Langevin and the…
We unify and generalize the notions of vacuum and amplitude in linear quantum field theory in curved spacetime. Crucially, the generalized notion admits a localization in spacetime regions and on hypersurfaces. The underlying concept is…