Renormalization of an effective Light-Cone QCD-inspired theory for the Pion and other Mesons

The renormalization of the effective QCD-Hamiltonian theory for the quark-antiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed point-Hamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of the renormalized effective QCD-Hamiltonian comes from the pion mass and radius, for a given constituent quark mass. The 1s and excited 2s states of $\bar u q$ are calculated as a function of the mass of the quark $q$ being s, c or b, and compared to the experimental values.Comment: 39 pages, 10 figure

On the Size of Hadrons

The form factor and the mean-square radius of the pion are calculated analytically from a parametrized form of a $q\bar q$ wave function. The numerical wave function was obtained previously by solving numerically an eigenvalue equation for the pion in a particular model. The analytical formulas are of more general interest than just be valid for the pion and can be generalized to the case with unequal quark masses. Two different parametrizations are investigated. Because of the highly relativistic problem, noticable deviations from a non-relativistic formula are obtained.Comment: 14 pages, minor typos corrected, several points clarified, results unchange

On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer- Duffin beta-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard `trace' techniques. The results are compared with a recent derivation due to Bosanac.Comment: 9 pages, Latex; email: [email protected]

Exact solutions to Pauli-Villars-regulated field theories

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, we also discuss how perturbation theory in the difference between the masses of the physical and Pauli-Villars particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions.Comment: 20 pages, REVTeX; minor corrections to normalization

Notices of Archaeological Publications

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Quantum Master Equation of Particle in Gas Environment

The evolution of the reduced density operator $\rho$ of Brownian particle is discussed in single collision approach valid typically in low density gas environments. This is the first succesful derivation of quantum friction caused by {\it local} environmental interactions. We derive a Lindblad master equation for $\rho$, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for $\rho$ is proved. Master equations proposed earlier are shown to be particular cases of our one.Comment: 6 pages PlainTeX, 23-March-199

Universal description of S-wave meson spectra in a renormalized light-cone QCD-inspired model

A light-cone QCD-inspired model, with the mass squared operator consisting of a harmonic oscillator potential as confinement and a Dirac-delta interaction, is used to study the S-wave meson spectra. The two parameters of the harmonic potential and quark masses are fixed by masses of rho(770), rho(1450), J/psi, psi(2S), K*(892) and B*. We apply a renormalization method to define the model, in which the pseudo-scalar ground state mass fixes the renormalized strength of the Dirac-delta interaction. The model presents an universal and satisfactory description of both singlet and triplet states of S-wave mesons and the corresponding radial excitations.Comment: RevTeX, 17 pages, 7 eps figures, to be published in Phys. Rev.

Noncommutative Gauge Theory on the q-Deformed Euclidean Plane

In this talk we recall some concepts of Noncommutative Gauge Theories. In particular, we discuss the q-deformed two-dimensional Euclidean Plane which is covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map is constructed to express noncommutative fields in terms of their commutative counterparts.Comment: 5 pages; Talk given by Frank Meyer at the 9th Adriatic Meeting, September 4th-14th, 2003, Dubrovni

Vacuum polarization induced by a uniformly accelerated charge

We consider a point charge fixed in the Rindler coordinates which describe a uniformly accelerated frame. We determine an integral expression of the induced charge density due to the vacuum polarization at the first order in the fine structure constant. In the case where the acceleration is weak, we give explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys