Related papers: Distance Domains: Continuity
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Recent progress in electro-optic sampling has allowed direct access to the fluctuations of the electromagnetic ground state. Here, we present a theoretical formalism that allows for an in-depth characterisation and interpretation of such…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
We discuss the classical limit for the long-distance (``soft'') modes of a quantum field when the hard modes of the field are in thermal equilibrium. We address the question of the correct semiclassical dynamics when a momentum cut-off is…
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a…
Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only if A is finite dimensional. We then show how one can explicitly build many quantum metrics with distinct domains on infinite-dimensional…
We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$.…
Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
In this note, we consider two types of estimates for the Harnack distance in bounded domains of a finite-dimensional Euclidean space. The first type is based on the geometric concept of the entropy of arcwise connectedness. We used this…
The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time…
We discuss thick domain walls interpolating between spaces with naked singularities and give arguments based on the $AdS$/CFT correspondence why such singularities may be physically meaningful. Our examples include thick domain walls with…
We introduce several homotopy equivalence relations for proper holomorphic mappings between balls. We provide examples showing that the degree of a rational proper mapping between balls (in positive codimension) is not a homotopy invariant.…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…
We show that most of cutoff measures of the multiverse violate some of the basic properties of probability theory when applied repeatedly to predict the results of local experiments. Starting from minimal assumptions, such as Markov…
Spherically complete ball spaces provide a framework for the proof of generic fixed point theorems. For the purpose of their application it is important to have methods for the construction of new spherically complete ball spaces from given…