Related papers: Dirac operator normality and chiral properties
A transformation is devised to convert any lattice Dirac fermion operator into a Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O(a) lattice…
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition…
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary…
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…
It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…
In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…
Nonperturbative Wilson coefficients associated with the leading chiral-symmetry-breaking operators in the operator product expansion of the pseudoscalar QCD correlation function are derived. Implementation of the new, instanton-induced…
Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
We study the quantization of chiral fermions coupled to generalized Dirac operators arising in NCG Yang-Mills theory. The cocycles describing chiral symmetry breaking are calculated. In particular, we introduce a generalized locality…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac…
We study particular classes of states on the Weyl algebra $\mathcal{W}$ associated with a symplectic vector space $S$ and on the von Neumann algebras generated in representations of $\mathcal{W}$. Applications in quantum physics require an…
The presence of chiral fermions in the physical Hilbert space implies consistency conditions on the spectral action. These conditions are equivalent to the absence of gauge and gravitational anomalies. Suggestions for the fermionic part of…
We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
We are interested in the consistency between the cutoff, chiral symmetry, and the power counting. For this purpose, we apply the Wilsonian renormalization group (RG) to an operator and then decrease the Wilsonian cutoff. As an example, we…