Related papers: Dirac operator on the quantum fuzzy four-sphere $ …
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the…
Three dimensional Dirac oscillator was considered in deformed space obeyed to deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations gives rise to appearance minimal uncertainty in position…
Starting from an even definite lattice, we construct a principal circle bundle covered by a certain three-step nilpotent Lie group G. On the base space, which is again a nilmanifold, we then study the Dirac operator twisted by the…
We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry. It is shown that these Dirac operators give rise to compact quantum metric…
In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Sigma and the…
We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term…
Using a new scaling limit as well as a new cut-off procedure, we show that $\phi^4$ theory on noncommutative ${\bf R}^4$ can be obtained from the corresponding theory on fuzzy ${\bf S}^2 \times {\bf S}^2$. The star-product on this…
The anomalous dimensions of four-quark operators $(\bar q_i q_j)_{V-A} (\bar q_k q_l)_{V-A}$ are calculated in the large $N_f$ limit. As expected, the result is a convergent series without renormalon ambiguities. Using the approximation of…
In this contribution we present results from quenched QCD simulations with the parameterized fixed-point (FP) and the chirally improved (CI) Dirac operator. Both these operators are approximate solutions of the Ginsparg-Wilson equation and…
We study an example of an index problem for a Dirac-like operator subject to Atiyah-Patodi-Singer boundary conditions on a noncommutative manifold with boundary, namely the quantum unit disk.
We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the…
This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the id\`ele class space, we place a…
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…
We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF…
The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…
We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.
We consider Dolbeault-Dirac operators on quantum projective spaces, following Krahmer and Tucker-Simmons. The main result is an explicit formula for their squares, up to terms in the quantized Levi factor, which can be expressed in terms of…
The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a…
We study spectra, localization properties and local chirality of eigenvectors of the lattice Dirac operator. We analyze ensembles of quenched SU(3) configurations on both sides of the QCD phase transition. Our Dirac operator is a systematic…