相关论文: A New Solution to Ginsparg-Wilson Relation from Ge…
Recent developments have shown that a lot can be gained for QCD simulations from GPU hardware. This can be exploited especially in the case of Ginsparg-Wilson fermions when the com putational costs are particularly high. In this work, we…
This paper is a mixture of expository material and current research material. Among new results are examples of generalised harmonic spinors and their gauged version, the generalised Seiberg-Witten equations.
In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single…
These notes explain recent developments concerning chiral anomalies and hamiltonian quantization, their relation to the theory of gerbes, and extensions of generalized loop algebras using the residue calculus of pseudodifferential…
We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the…
In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes $\mathrm{AI}^\dagger$ and $\mathrm{AII}^\dagger$. We show that the continuum Dirac…
The Ginsparg-Wilson relation is extended to interacting field theories with general linear symmetries. Our relation encodes the remnant of the original symmetry in terms of the blocked fields and guides the construction of invariant lattice…
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…
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…
We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of…
We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators,…
A new class of lattice Dirac operators $D$ which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$…
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…
We launched a project to perform dymanical fermion simulations using the overlap fermion formulation for sea quarks. In order to avoid the appearace of near-zero modes of the hermitian Wilson-Dirac operator $H_W$, we introduce a pair of…
The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…
Recently, two solutions have been proposed to the long standing problem of $\mathcal{CP}$-symmetry on the lattice, which is particularly evident when considering the construction of chiral gauge theories. The first, based on a lattice…
An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted…
The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.
A manifestly gauge invariant formulation of chiral theories with fermions on the lattice is developed. It combines SLAC lattice derivative \cite{DWY}, \cite{ACS}, \cite{S} and generalized Pauli-Villars regularization \cite{FS}. The theory…