Related papers: A nonlocal discretization of fields
Light and heavy-light (b) hadrons are among the most interesting and among the most challenging quantities to calculate in lattice gauge theory. One would like to avoid discretization effects from very heavy quarks and to calculate chiral…
In this paper the local differential calculus over Fedosov algebra is constructed using the trivialization isomorphism. The explicit formulas for deformed derivations are given. The resulting calculus can be used as a "building block" for a…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific…
Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known…
In this paper I propose the use of a lattice derivative operator that is equivalent to the ideal SLAC derivative operator in all lattice calculations, but without the prohibitively expensive computational cost of the latter. A pedagogical…
To connect conformal field theories (CFT) to probabilistic lattice models, recent works [HKV22, Ada23] have introduced a novel definition of local fields of the lattice models. Local fields in this picture are probabilistically concrete:…
Considering a theory space consisting of a large number of five-dimensional Dirac fermion field theories including background abelian gauge fields, we can construct a theory similar to a continuous six-dimensional theory compactified with…
We have proposed a lattice SUSY formulation which we may call super doubler approach, where chiral fermion species doublers and their bosonic counter parts are either identified as super partners or truncated by chiral conditions. We claim…
We propose a geometric formulation of effective field theories via nonlinear supersymmetry. Non-supersymmetric particles are embedded in constrained superfields governed by a nonlinear sigma model, and operators are collected into…
The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite…
We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow…
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…
The light--cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice Hamiltonian written in terms of discrete fermi fields. Several subtle points concerning boundary conditions,…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Our review of the lattice chiral fermion delves into some critical areas of lattice field theory. By abandoning Hermiticity, the non-Hermitian formulation circumvents the Nielsen-Ninomiya theorem while maintaining chiral symmetry, a novel…
A popular approximation in lattice gauge theory is an extrapolation in the number of fermion species away from the four fold degeneracy natural with the staggered fermion formulation. I show that the extrapolation procedure mutilates the…
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We give again the proof of several classical results concerning the cyclotomic approach to Fermat's last theorem using exclusively class field theory (essentially the reflection theorems), without any calculations. The fact that this is…