Related papers: Dirac-Kaehler fermion with noncommutative differen…
In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\S)\to…
We demonstrate that in the topologically trivial gauge sector the Ginsparg-Wilson relation for lattice Dirac operators admits an exactly gauge invariant path integral formulation of the Weyl fermions on a lattice.
The $SU(N_f)_L \otimes SU(N_f)_R$ chiral symmetry of QCD is of central importance for the nonperturbative low-energy dynamics of light quarks and gluons. Lattice field theory provides a theoretical framework in which these dynamics can be…
The Nielson-Ninomiya theorem states that a chirally invariant free fermion lattice action, which is local, translation invariant, and real necessarily has fermion doubling. The SLAC approach gives up on locality and long range hopping leads…
We propose a formulation of lattice fermions with one-sided differences that is hermitian, chirally symmetric (barring a bare mass term) and completely free of doubling. To obtain the axial anomaly in perturbation theory it was necessary to…
In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by…
We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the…
Prompted by a recent demonstration that the structure of a single quark-lepton generation may be understood via a Dirac-like linearization of the form p^2+x^2, we analyze the corresponding Clifford algebra in some detail. After classifying…
A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…
In the light-front formulation of field theory, it is possible to write down a chirally invariant mass term. It thus appears as if one could solve the species doubling problem on a light-front quantized transverse lattice in a chirally…
We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. We define (p,q)-left- and right-monogenic functions by means of Dirac operators that factor a certain wave operator. We prove…
We study K\"ahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the…
We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and…
In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator,…
In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the Hamiltonian formalism to nonabelian difference…
Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed…
We describe a novel way to think about bosonic lattice theories in Hamiltonian form where each lattice site has only a half boson degree of freedom. The construction requires a non-trivial Poisson bracket between neighboring sites and leads…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $\epsilon$-regime of QCD. This correlation function has a unique and strong dependence on $F_\pi$, and thus provides an novel…
We pursue Ginsparg and Wilsons' block spin approach in the derivation of the Ginsparg-Wilson relation and study the correspondence of the eigenmodes of the Dirac operators in the continuum and lattice theories. After introducing a suitable…