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

In our previous paper (hep-th/9911087), we proposed a resolution for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its cartesian products. In this paper after a review of that work, we bring out its…

The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have…

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…

The fermion doubling problem has an important impact on quantum gravity, by revealing the tension between fermion and the fundamental discreteness of quantum spacetime. In this work, we discover that in Loop Quantum Gravity, the quantum…

In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories…

In this talk we give a brief description of the formulation of chiral and gauge symmetries on the fuzzy sphere . In particular fermion doublers are shown to be absent and the correct anomaly equation in two dimensions is obtained in the…

We derive the spherical field formalism for fermions. We find that the spherical field method is free from certain difficulties which complicate lattice calculations, such as fermion doubling, missing axial anomalies, and computational…

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 propose a procedure for computing noncommutative corrections to the metric tensor, and apply it to scalar field theory written on coordinate patches of smooth manifolds. The procedure involves finding maps to the noncommutative plane…

We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between…

We discuss some aspects of a new noncombinatorial fermionic approach to the two-dimensional dimer problem in statistical mechanics based on the integration over anticommuting Grassmann variables and factorization ideas for dimer density…

A new formulation for fermions on the lattice based on a discretization of a second order formalism is proposed. A comparison with the first order formalism in connection with the $U(1)$ anomaly and the doubling problem is presented. The…

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was…

The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come in pairs in three-dimensional semimetals. Here, we present an extension of the doubling theorem to…

We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make…

We study a noncommutative gauge theory on a fuzzy four-sphere. The idea is to use a matrix model with a fifth-rank Chern-Simons term and to expand matrices around the fuzzy four-sphere which corresponds to a classical solution of this…

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by…

This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed,…

In continuum physics, there are important topological aspects like instantons, theta-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we…

In this paper we propose a new approach to formulate the field theory on a lattice. This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation for both Fermion and Boson…