相关论文: The Fermion Doubling Problem and Noncommutative Ge…

It is possible to characterize certain states of matter by properties of their edge states. This implies a notion of `surface-only models': models which can only be regularized at the edge of a higher-dimensional system. After incorporating…

We consider a set of physical degrees of freedom coupled to a finite-dimensional Hilbert space, which may be taken as modeling a fuzzy space or as the lowest Landau level of a Landau-Hall problem. These may be viewed as matter fields on a…

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and…

We study the second quantization of field theory on the q-deformed fuzzy sphere for real q. This is performed using a path-integral over the modes, which generate a quasiassociative algebra. The resulting models have a manifest U_q(su(2))…

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…

The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…

The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of…

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…

The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for…

We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…

In this paper, we discuss two features of the noncommmutative geometry and spectral action approach to the Standard Model: the fact that the model is inherently Euclidean, and that it requires a quadrupling of the fermionic degrees of…

We address the variational preparation of the Thermofield Double as the ground state of a suitably engineered Hamiltonian acting on the doubled Hilbert space. Through the use of the Entanglement Forging ansatz, we propose a solution that…

In contrast to the non-relativistic approaches, three-dimensional (3D) mesh calculations for the {\it relativistic} density functional theory have not been realized because of the challenges of variational collapse and fermion doubling. We…

Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…

We study, via bosonization, the Landau fixed point for the problem of interacting spinless fermions near the Fermi surface in dimensions higher than one. We rederive the bosonic representation of the Fermi operator and use it to find the…

A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion…

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a…

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…

The enveloping algebra,$D_{n}$,of fermions is extended on the lattice to include the discrete space invariance.This extended algebra,denoted X, has the space symmetry as a factor : $X/D_{n}$ = space group.

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and…