ar X iv : m at h - ph / 0 30 60 62 v 1 2 5 Ju n 20 03 VECTOR COHERENT STATES WITH AN UNBOUNDED INVERSE FRAME OPERATOR

ar X iv : m at h - ph / 0 20 60 17 v 1 1 2 Ju n 20 02 Z 3 - graded Grassmann Variables , Parafermions and their Coherent States

A relation between the Z3-graded Grassmann variables and parafermions is established. Coherent states are constructed as a direct consequence of such a relationship. We also give the analog of the Bargmann-Fock representation in terms of these Grassmann variables.

ar X iv : h ep - l at / 0 30 60 33 v 1 2 5 Ju n 20 03 Fermions in 2 D Lorentzian Quantum Gravity

We implement Wilson fermions on 2D Lorentzian triangulation and determine the spectrum of the Dirac-Wilson operator. We compare it to the spectrum of the corresponding operator in the Euclidean background. We use fermionic particle to probe the fractal properties of Lorentzian gravity coupled to c = 1/2 and c = 4 matter. We numerically determine the scaling exponent of the mass gap M ∼ N −1/dH ...

ar X iv : m at h - ph / 0 30 60 72 v 1 2 7 Ju n 20 03 Symmetries and currents of massless neutrino fields , electromagnetic and graviton fields

A recent complete, explicit classification of all locally constructed symmetries and currents for free spinorial massless spin s fields on Minkowski space is summarized and extended to give a classification of all covariant symmetry operators and conserved tensors. The results, for physically interesting cases, are also presented in tensorial form for electromagnetic and graviton fields (s = 1,...

ar X iv : m at h - ph / 0 30 10 19 v 1 1 5 Ja n 20 03 Which distributions of matter diffract ? — Some answers

ar X iv : m at h / 05 06 60 5 v 1 [ m at h . Q A ] 2 9 Ju n 20 05 Convergence of the Wick Star Product

We construct a Fréchet space as a subspace of Cω(Cn) where the Wick star product converges and is continuous. The resulting Fréchet algebra A~ is studied in detail including a ∗-representation of A~ in the Bargmann-Fock space and a discussion of star exponentials and coherent states.