Related papers: Relativistic Propagators on Lattices
A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step…
Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. In this work we introduce a simple technique to generate arbitrary dispersion relations in a modulated tilted lattice. The technique is…
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\mathbb{Z}^2$. We first prove a formula on the rotation number of a…
We discuss general positivity conditions necessary for a definition of a relativistic diffusion on the phase space. We show that Lorentz covariant random vector fields on the forward cone $p^{2}\geq 0$ lead to a definition of a generator of…
Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…
In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For…
The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a…
We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…
We calculate the transverse and time-time components of the instantaneous gluon propagator in Coulomb gauge QCD by using an SU(3) quenched lattice simulation on isotropic and anisotropic lattices. We find that the gluon propagators suffer…
We present a direct path integral derivation of the propagator in the presence of a step potential. The derivation makes use of the Path Decomposition Expansion (PDX), and also of the definition of the propagator as a limit of lattice…
Recent lattice computations showed how the approach dubbed "refined Gribov-Zwanziger scenario" is in very good agreement with data and the gluon propagator fits them very well. This propagator can be described as a finite sum of Yukawa…
We study the representations of non-commutative universal lattices and use them to compute lower bounds for the \TauC for the commutative universal lattices $G_{d,k}= \SL_d(\Z[x_1,...,x_k])$ with respect to several generating sets. As an…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
Green's functions are gauge-dependent quantities. Thus, the manifestation of confinement in these correlation functions also depends on the gauge. Here we use lattice gauge theory to study the gluon and the ghost propagators in a gauge (the…
In this article, we extend our previously presented analytical formulas (Phys.Rev.D 109 (2024) 12, 124055) for describing light rays passing near or emitted in the vicinity of compact objects to a broader class of spherically symmetric,…
We discuss the superluminal problem in the diffusion of ultra high energy protons with energy losses taken into account. The phenomenological solution of this problem is found with help of the generalized J\"uttner propagator, originally…
Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results…
We evaluate numerically the four-momentum-space gluon propagator in lattice Landau gauge, for pure SU(2) lattice gauge theory with periodic boundary conditions. Simulations are done in the strong-coupling regime, namely at $\beta = 0, 0.8,…
We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition methods. The diffusion coefficient can be arbitrarily rough in…
We consider the massive Klein-Gordon equation on asymptotically Minkowski spacetimes, in the sense that the manifold is $R^{1+d}$ and the metric approaches that of Minkowski space at infinity in a short-range way (jointly in time and space…