For the q-deformed canonical commutation relations a(f)a † (g) = (1 − q) f, g1I + q a † (g)a(f) for f, g in some Hilbert space H we consider representations generated from a vector Ω satisfying a(f)Ω = f, ϕΩ, where ϕ ∈ H. We show that such a representation exists if and only if ϕ ≤ 1. Moreover, for ϕ < 1 these representations are unitarily equivalent to the Fock representation (obtained for ϕ =...

The v-function is a key ingredient in the wild McKay correspondence. In this paper, we give formula to compute it terms of valuations Witt vectors, when given group cyclic prime power order. We apply study singularities quotient variety by square criterion whether stringy motive converges or not. Furthermore, if representation indecomposable, then also simple for being terminal, canonical, log ...

Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being discretization Euclidian time. Convergence time-continuum limit is shown various discretized actions. The focus integral representation partition function and expectation values in canonical ensemble. connection to grand-canonical integral, number differences, dis...

We study a canonical model of type-I membranes subject to correlated fluctuating input currents. We present a semi-analytical approach for calculating the response of this neuron model to time dependent inputs both in the input current and the noise amplitude using a novel sparse matrix representation of the systems Fokker–Planck operator. It turns out, that the maximum stimulation frequency wh...

A general pedagogical survey of the basics of the Bethe-Salpeter equation and in particular Wick-Cutkosky model is given in great technical details. The Bethe-Salpeter approach to the relativistic two-body bound state problem assumes that all needed information about a bound state |B > is contained in the B-S amplitude Φ(x 1 , x 2 ; P B) =< 0|T φ 1 (x 1)φ 2 (x 2)|B > (1) and in its conjugate ¯ ...

For any finite graph Γ and any field K of characteristic unequal to 2 we construct an algebraic variety X over K whose K-points parameterise K-Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with prescribed commutation relations, corresponding to the non-edges. After that, we study the case where Γ is a connected, simply laced Dynkin diagram of finite or...

It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {eii}I with each ēii in the center of Λ̄ = Λ/r iff Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given. As a corollary, Λ is a finite algebra with non-zero unity element over perfect field k (e.g. a field ...

We propose a canonical representation of the long run matrix, which can constitute a basis for non-causality testing. This representation requires to determine a sub-matrix rank, which can be done using a test procedure, whose properties are analysed with Monte Carlo experiments.  2000 Elsevier Science S.A. All rights reserved.

We propose a canonical representation of the long run matrix, which can constitute a basis for non-causality testing. This representation requires to determine a sub-matrix rank, which can be done using a test procedure, whose properties are analysed with Monte-Carlo experiments.  2000 Elsevier Science S.A. All rights reserved.

Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra O2. As examples, we show fermionizations on the Fock space and the infinite wedge. Mathematics Subject Classifications (2000). 46K10, 46L60