Renormalization and Essential Singularity

In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of renormalization, including quantum gravity. As an example, we classify possible singularities of a potential for the Schr\"{o}dinger equation, assuming that the potential V has at least one $C^2$ class eigen function. The result crucially depends on the analytic property of the eigen function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail

Towards reliable calculations of the correlation function

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.Comment: 18 pages, presented at XIth International Workshop on Correlation and Fluctuation in Multiparticle Production, Hangzhou, China, November 21-24, 200

Bosonization solution of the Falicov-Kimball model

We use a novel approach to analyze the one dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states; we find a crossover between the well-known weak- and strong-coupling behaviour. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.Comment: RevTex, 10 pages, 1 figur

Adiabatic theorems for linear and nonlinear Hamiltonians

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation. It is shown that in some cases the found condition is necessary and sufficient. The adiabatic theorem is generalized for the case of nonlinear Hamiltonians

Gauge transformation through an accelerated frame of reference

The Schr\"{o}dinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.Comment: 7 Pages, Latex fil

Gauge invariance and non-constant gauge couplings

It is shown that space-time dependent gauge couplings do not completely break gauge invariance. We demonstrate this in various gauge theories.Comment: 18 page

The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation

The usual quantitative condition has been widely used in the practical applications of the adiabatic theorem. However, it had never been proved to be sufficient or necessary before. It was only recently found that the quantitative condition is insufficient, but whether it is necessary remains unresolved. In this letter, we prove that the quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation.Comment: 4 pages,1 figue

Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Di\'osi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calculated by a classical Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references added 9/29/06: further minor revisions and references adde

Equivalence Theorems for Pseudoscalar Coupling

By a unitary transformation a rigorous equivalence theorem is established for the pseudoscalar coupling of pseudoscalar mesons (neutral and charged) to a second-quantized nucleon field. By the transformation the linear pseudoscalar coupling is eliminated in favor of a nonlinear pseudovector coupling term together with other terms. Among these is a term corresponding to a variation of the effective rest mass of the nucleons with position through its dependence on the meson potentials. The question of the connection of the nonlinear pseudovector coupling with heuristic proposals that such a coupling may account for the saturation of nuclear forces and the independence of single nucleon motions in nuclei is briefly discussed. The new representation of the Hamiltonian may have particular value in constructing a strong coupling theory of pseudoscalar coupled meson fields. Some theorems on a class of unitary transformations of which the present transformation is an example are stated and proved in an appendix.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86126/1/PhysRev.87.1061-RKO.pd