Aliasing modes in the lattice Schwinger model

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass.Comment: Enlarged version, 1 figure added, 11 page

Finite-size effects on a lattice calculation

We study in this paper the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.Comment: 8 pages, no figures, extended version, five references adde

Free fermionic propagators on a lattice

A method used recently to obtain a formalism for classical fields with non-local actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens' principle with free discrete propagators that recover their continuum forms in certain limit.Comment: LaTex document, 13 pages, 1 figure. Minor changes, two references adde

Neutrino damping rate at finite temperature and density

A first principle derivation is given of the neutrino damping rate in real-time thermal field theory. Starting from the discontinuity of the neutrino self energy at the two loop level, the damping rate can be expressed as integrals over space phase of amplitudes squared, weighted with statistical factors that account for the possibility of particle absorption or emission from the medium. Specific results for a background composed of neutrinos, leptons, protons and neutrons are given. Additionally, for the real part of the dispersion relation we discuss the relation between the results obtained from the thermal field theory, and those obtained by the thermal average of the forward scattering amplitude.Comment: LaTex Document, 19 pages, 3 figure

非平衡量子系への情報理論のアプローチ(第9回『非平衡系の統計物理』シンポジウム,研究会報告)

この論文は国立情報学研究所の電子図書館事業により電子化されました。我々は情報理論を量子場の非平衡ダイナミクスに当てはめた。この方法は最大エントロピー法のJaynes-Gibbs原理と初期値データをグリーン関数の運動方程式に入れることにより得られる結果に基づいている。この方法が有効であるかを示すために、O(N)φ^4理論をNの1次までで用い時間・空間不変性を持つ系の圧力を計算した。We apply the information theory to the non-equilibrium dynamics of quantum fields. Our approach is based on the Jaynes-Gibbs principle of the maximal entropy and its implementation, throughout the initial-value data, into the dynamical equations for Green's functions. To show how our method works we employ the O(N) φ^4 theory in the leading N-order and calculate the pressure for a system which is invariant under both spatial and temporal translations