The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2(Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investiga...

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scalin...

The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2 (Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investig...

An extraordinary strong magnetic field, eB0≈1018 Gauss, is expected to be generated in non-central ultrarelativistic heavy ion collisions and it envisaged induce several effects on hot QCD matter including the possibility of local parity charge conjugation symmetry violations. A direct signature such e.m. fields a first quantitative measurement its strength lifetime are still missing. We point ...

Classes of objects injective w.r.t. specified morphisms are known to be closed under products and retracts. We prove the converse: a class of objects in a locally presentable category is an injectivity class iff it is closed under products and retracts. This result requires a certain large-cardinal principle. We characterize classes of objects injective w.r.t. a small collection of morphisms: t...

Cattani–Sassone’s notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled n-cube turns out to be the free higher dimensional transition system generated by one n-dimensional...

Cattani-Sassone’s notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled n-cube turns out to be the free higher dimensional transition system generated by one n-dimensional...

For a locally presentable abelian category B with projective generator, we construct the derived and contraderived model structures on of complexes, proving in particular existence enough homotopy complexes objects. We also show that D(B) is generated, as triangulated coproducts, by generator B. Grothendieck A, injective coderived complexes. Assuming Vopěnka's principle, prove D(A) products, co...

We show, for a monoidal closed category V = (V0,⊗, I), that the category V -Cat of small V -categories is locally λ-presentable if V0 is so, and that it is locally λ-bounded if the closed category V is so, meaning that V0 is locally λ-bounded and that a side condition involving the monoidal structure is satisfied. Many important properties of a monoidal category V are inherited by the category ...

Following an idea of D. Bennequin, we give a classiication of quadratic algebras generated by creation and destruction operators, in which the Heisenberg equations of motion for a system of harmonic oscillators hold. For simplicity of exposition, we x K = C, the eld of complex numbers, but all the results would be valid for any commutative eld of characteristic 0, endowed with an involution (po...