Related papers: Localization of nonlocal theories
A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations…
We study the Cauchy problem for non-linear non-local operators that may be degenerate. Our general framework includes cases where the jump intensity is allowed to depend on the values of the solution itself, e.g. the porous medium equation…
Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the…
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
A classical statistical field theory hidden variable model for the quantized Klein-Gordon model is constructed that preserves relativistic signal locality and is relativistically covariant, but is at the same time relativistically nonlocal,…
We prove a general local existence theorem for nonlinear systems of Cauchy-Riemann operator of any order in one complex variable with initial values at a given point, which is a counterpart of local existence of ODE.
We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of…
We study the covariant free bosonic string field theory and explore its locality (causality) properties. We find covariant string fields which are strictly local and covariant, but act on an unconstrained Hilbert space with an indefinite…
We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…
Discovery of mathematical descriptors of physical phenomena from observational and simulated data, as opposed to from the first principles, is a rapidly evolving research area. Two factors, time-dependence of the inputs and hidden…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in…
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be…
Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition,…
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
Recent results on the effective non-local dynamics of the tachyon mode of open string field theory (OSFT) show that approximate solutions can be constructed which obey the diffusion equation. We argue that this structure is inherited from…
We impose in the nonsymmetric gravitational theory, by means of Lagrange multiplier fields in the action, a set of covariant constraints on the antisymmetric tensor field. The canonical Hamiltonian constraints in the weak field…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…