Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential

We have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis. We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known "sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations.Comment: 7 pages, presented at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Sardinia, Italy, June 14-19, 201

Transfer matrix for Kogut-Susskind fermions in the spin basis

In the absence of interaction it is well known that the Kogut-Susskind regularizations of fermions in the spin and flavor basis are equivalent to each other. In this paper we clarify the difference between the two formulations in the presence of interaction with gauge fields. We then derive an explicit expression of the transfer matrix in the spin basis by a unitary transformation on that one in the flavor basis which is known. The essential key ingredient is the explicit construction of the fermion Fock space for variables which live on blocks. Therefore the transfer matrix generates time translations of two lattice units.Comment: 16 page

Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD

We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle point approximations live fermionic quasiparticles with quark quantum numbers which are confined, in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of mesons-nucleons action is outlined.Comment: 33 page

Quark-composites approach to QCD

We present a perturbative approach to QCD based on quark composites, that is barions and mesons, as fundamental variables.Comment: 4 pages LaTeX, to appear in the proceedings of ``Path Integrals from peV to TeV'', Florence-Italy, August 25-29, 199

Секвенційні числення композиційно-номінативних модальних логік функціонально-екваційного рівня

Досліджуються композиційно-номінативні модальні та темпоральні логіки функціонально-екваційного рівня. На основі властивостей відношення логічного наслідку для множин формул збудовані числення секвенційного типу для загальних та темпоральних композиційно-номінативних модальних логік такого рівня. Для побудованих числень доведені теореми коректності та повноти

Higher order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries

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General perturbative approach to the diffusion equation in the presence of absorbing defects: frequency-domain and time-domain results

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