Related papers: A nonlocal discretization of fields
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or…
We present a theoretical framework on non-local classical field theory using fractional integrodifferential operators. Due to the lack of easily manageable symmetries in traditional fractional calculus and the difficulties that arise in the…
We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the…
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply…
The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In prior work we have shown how to overcome this limitation for classical actions…
Using the method of finite differences a scheme is proposed to solve exactly the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional lattice. The hamiltonian of the Dirac field is translational invariant, hermitian, avoids…
To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…
We use a specific implementation of discrete differential geometry to describe Dirac-Kahler fermions in such a way that we can separate their chiral and flavour components. The formulation introduces additional lattices so that on each…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
We propose a discretisation scheme based on the Dirac-Kahler formalism (DK) in which the algebraic relations between continuum operators ${\wedge, d, \star}$ are captured by their discrete analogues, allowing the construction of the…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as…
A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the…
By placing fermions only on the even sites of a lattice, one may halve the momentum spectrum and construct a theory without doublers. The interaction is nonlocal. The fermion propagator is not a sparse matrix, but because the unwanted…
A new multifermion formulation of lattice QCD is proposed. The model is free of spectrum doubling and preserves all nonanomalous chiral symmetries up to exponentially small corrections. It is argued that a small number of fermion fields may…
In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type…
A new approach to formulate the fermion field on lattice is introduced by proposing a new Dirac operator on lattice.This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation…
A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral…
We present a new method for regularizing chiral theories on the lattice. The arbitrariness in the regularization is used in order to decouple massless replica fermions. A continuum limit with only one fermion is obtained in perturbation…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…