A Possible Way of Connecting the Grassmann Variables and the Number of Generation

We construct a Left-Right symmetric model in which the number of generation is related to Grassmann variables. We introduce two sets of complex Grassmann variables ($\theta^1_q$,$\theta^2_q$), ($\theta^1_l$, $\theta ^2_l$) and associate each variable with left- and right-handed quark and lepton fields, respectively. Expanding quark and lepton fields in powers of the Grassmann variables, we find that there are exactly three generations of quarks and leptons. Integrating out the Grassmann variables, we obtain phenomenologically acceptable fermion mass matrices.Comment: 7 pages, Revtex, UM-P-93/40, OZ-93/1

The Negative Dimensional Oscillator at Finite Temperature

We study the thermal behavior of the negative dimensional harmonic oscillator of Dunne and Halliday that at zero temperature, due to a hidden BRST symmetry of the classical harmonic oscillator, is shown to be equivalent to the Grassmann oscillator of Finkelstein and Villasante. At finite temperature we verify that although being described by Grassmann numbers the thermal behavior of the negative dimensional oscillator is quite different from a Fermi system.Comment: 8 pages, IF/UFRJ/93/0

Quark gap equation within the analytic approach to QCD

The compatibility between the QCD analytic invariant charge and chiral symmetry breaking is examined in detail. The coupling in question incorporates asymptotic freedom and infrared enhancement into a single expression, and contains only one adjustable parameter with dimension of mass. When inserted into the standard form of the quark gap-equation it gives rise to solutions displaying singular confining behavior at the origin. By relating these solutions to the pion decay constant, a rough estimate of about 880 MeV is obtained for the aforementioned mass-scale.Comment: Talk given by J.P. at 12th International QCD Conference (QCD05), 4 - 9 July 2005, Montpellier, France; 4 pages, 3 figure

Heavy quark supermultiplet excitations

Lorentz covariant wave functions for meson and baryon supermultiplets are simply derived by boosting $SU(2)_J$ representations corresponding to multiquark systems at rest.Comment: 12 pages (Revtex), UTAS-PHYS-93-4

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte

Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation

Based on the path integral formalism, we rederive and extend the transverse Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger-Dyson equation in which the the transverse Ward-Takahashi identity together with the usual (longitudinal) Ward-Takahashi identity are applied to specify the fermion-boson vertex function. Especially, in two dimensional Abelian gauge theory, we show that this scheme leads to the exact and closed Schwinger-Dyson equation for the fermion propagator in the chiral limit (when the bare fermion mass is zero) and that the Schwinger-Dyson equation can be exactly solved.Comment: 22 pages, latex, no figure

3-point off-shell vertex in scalar QED in arbitrary gauge and dimension

We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for Scalar Quantum Electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose non-perturbative forms of this vertex that coincide with the perturbative answer to order $e^2$.Comment: Uses axodra

Four-point Green functions in the Schwinger Model

The evaluation of the 4-point Green functions in the 1+1 Schwinger model is presented both in momentum and coordinate space representations. The crucial role in our calculations play two Ward identities: i) the standard one, and ii) the chiral one. We demonstrate how the infinite set of Dyson-Schwinger equations is simplified, and is so reduced, that a given n-point Green function is expressed only through itself and lower ones. For the 4-point Green function, with two bosonic and two fermionic external `legs', a compact solution is given both in momentum and coordinate space representations. For the 4-fermion Green function a selfconsistent equation is written down in the momentum representation and a concrete solution is given in the coordinate space. This exact solution is further analyzed and we show that it contains a pole corresponding to the Schwinger boson. All detailed considerations given for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure

Conformal Symmetry and the Three Point Function for the Gravitational Axial Anomaly

This work presents a first study of a radiative calculation for the gravitational axial anomaly in the massless Abelian Higgs model. The two loop contribution to the anomalous correlation function of one axial current and two energy-momentum tensors, , is computed at an order that involves only internal matter fields. Conformal properties of massless field theories are used in order to perform the Feynman diagram calculations in the coordinate space representation. The two loop contribution is found not to vanish, due to the presence of two independent tensor structures in the anomalous correlator.Comment: 34 pages, 5 figures, RevTex, Minor changes, Final version for Phys. Rev.

A square root of the harmonic oscillator

Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalizations.Comment: RevTex, 10 pages in preprint form, no figure