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

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

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

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

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

Interference in Bohmian Mechanics with Complex Action

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP {125}, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods -- the propagation of wavefunctions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that pose severe difficulties for existing numerical schemes. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods

Lukewarm black holes in quadratic gravity

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon

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]