Related papers: Localization of nonlocal theories
Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular,…
The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this…
This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator. Our proof for uniqueness is based upon the analysis on a…
We consider scalar field theory defined over a direct product of the real and $p$-adic numbers. An adjustable dynamical scaling exponent $z$ enters into the microscopic lagrangian, so that the Gaussian theories provide a line of fixed…
This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for…
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…
We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and a generalized Noether theorem, we define the canonical…
This work deals with the presence of localized structures in relativistic systems described by two real scalar fields in two-dimensional spacetime. We consider the usual two-field model with the inclusion of the cuscuton term, which couples…
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
We consider the loop space representation of multi-matrix models. Explaining the origin of a time variable through stochastic quantization we make contact with recent proposals of Ishibashi and Kawai. We demonstrate how collective field…
Bell nonlocality is an intriguing property of quantum mechanics with far reaching consequences for information processing, philosophy and our fundamental understanding of nature. However, nonlocality is a statement about static correlations…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the…
We present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast, the coupling to the remaining balance laws involves a…
We study a class of nonlocal reaction-diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic…
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…
We suggest a conformally invariant generalization of string theory to higher-dimensional objects. As such a model, we consider a conformally invariant $\sigma$ model. For this theory, the Hamiltonian formalism is constructed, and the full…
In quantum field theory, the rigorous construction of local observables in the presence of nontrivial interaction is a crucial problem. In a class of integrable quantum field theories, a very abstract existence proof has recently been given…