Related papers: A note on the lattice Dirac-Kaehler equation
Tensor, matrix and quaternion formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The…
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…
A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then…
We use 1+1 dimensional large N Gross-Neveu models as a laboratory to derive microscopically effective Lagrangians for positive energy fermions only. When applied to baryons, the Euler-Lagrange equation for these effective theories assumes…
We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different…
We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge-Riemann theorem for compact Kaehler manifolds.
Exactly solvable (spinless) lattice fermions with wide range interactions are constructed explicitly based on {\em exactly solvable stationary and reversible Markov chains} $\mathcal{K}^R$ reported a few years earlier by Odake and myself.…
The sign problem is a major obstacle to our understanding of the phase diagram of QCD at finite baryon density. Several numerical methods have been proposed to tackle this problem, but a full solution to the sign problem is still elusive.…
This paper proposes SU(2)-gauge-invariant field equations involving interaction with a scalar field. A connection with the Dirac equation is discussed.
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…
A relationship between the discrete Dirac-K\"ahler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete Dirac-K\"ahler equation can be…
In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…
Cooper problem for interacting fermions is solved in a lattice. It is found that the binding energy of the Cooper problem can behave qualitatively differently from the gap parameter of the BCS theory and that pairs of non-zero center of…
Tensor and matrix formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection…
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…
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great…
We discuss lattice methods to obtain the derivatives of a lattice meson mass with respect to the bare sea and valence quark masses. Applications are made to quenched and dynamical fermion configurations. We find evidence for significant…
We develop and test a spectral-density analysis method, based on the introduction of smeared energy kernels, to extract physical information from two-point correlation functions computed numerically in lattice field theory. We apply it to a…
We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas…
We perform the first study of treating b, c, and s quarks as Dirac fermions in lattice QCD with exact chiral symmetry. On a 32^3 60 lattice with 1/a ~ 7.68 GeV, we compute point-to-point quark propagators, and measure the time-correlation…