Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

Might EPR particles communicate through a wormhole?

We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.Comment: Corrected version, to appears in EP

On the Relationship between Resolution Enhancement and Multiphoton Absorption Rate in Quantum Lithography

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a ``NOON'' quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated, in order to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.Comment: 14 pages, 7 figures, submitted, v2: rewritten in response to referees' comments, v3: rewritten and extended, v4: accepted by Physical Review

Gauge-Invariant Approach to Meson Photoproduction Including the Final-State Interaction

A gauge-invariant formalism is presented for the practical treatment of photo- and electroproduction of pseudoscalar mesons off nucleons that allows an explicit incorporation of hadronic final-state interactions. The semi-phenomenological approach is based on a field theory developed by one of the authors. It generalizes an earlier approach by allowing for systematic improvement of approximations in a controlled manner. The practical feasibility is illustrated by applying the lowest-order result to the photoproduction of both neutral and charged pions.Comment: Plenary talk given at the N*2005 Workshop (Oct. 2005, Tallahassee, FL); to appear in the Proceedings (to be publ. by WorldScientific

Relating on-shell and off-shell formalism in perturbative quantum field theory

In the on-shell formalism (mostly used in perturbative quantum field theory) the entries of the time ordered product T are on-shell fields (i.e. the basic fields satisfy the free field equations). With that, (multi)linearity of T is incompatible with the Action Ward identity. This can be circumvented by using the off-shell formalism in which the entries of T are off-shell fields. To relate on- and off-shell formalism correctly, a map sigma from on-shell fields to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In that paper it was shown that, in the case of one real scalar field in N=4 dimensional Minkowski space, these axioms have a unique solution. However, this solution was given there only recursively. We solve this recurrence relation and give a fully explicit expression for sigma in the cases of the scalar, Dirac and gauge fields for arbitrary values of the dimension N.Comment: The case of gauge fields was added. 16 page

The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds

A new approach to the concept of particles and their production in quantum field theory is developed. A local operator describing the current of particle density is constructed for scalar and spinor fields in arbitrary gravitational and electromagnetic backgrounds. This enables one to describe particles in a local, general-covariant and gauge-invariant way. However, the current depends on the choice of a 2-point function. There is a choice that leads to the local non-conservation of the current in a gravitational or an electromagnetic background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. The most natural choice based on the Green function calculated using the Schwinger-DeWitt method leads to the local conservation of the current, provided that interactions with quantum fields are absent. Interactions with quantum fields lead to the local non-conservation of the current which describes local particle production consistent with the usual global description based on the interaction picture.Comment: 34 pages, revised, to appear in Int. J. Mod. Phys.

Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic field

The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas unitary transformation approach is used when managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed to a much more simple system that is the sum of two independent harmonic oscillators which have time-dependent frequencies. We therefore easily identified the wave functions in the transformed system with the help of invariant operator of the system. The full wave functions in the original system is derived from the inverse unitary transformation of the wave functions associated to the transformed system.Comment: 16 page

Current conservation, screening and the magnetic moment of the Δ\Delta resonance. -- 1. Formulation without quark degrees of freedom

The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is studied in a new form of current conservation. According to this condition, the internal and external particle radiation parts of the $\pi N$ radiation amplitude have opposite signs, i.e., they contain terms which must cancel each other. Therefore, one has a screening of the internal and external particle radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex cancel against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances and the anomalous magnetic moment of the proton $\mu_p$ is obtained, where $\mu_{\Delta}$ is expressed by $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement with the values extracted from the fit for the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.Comment: 37 pages, 2 figures and 1 tabl

Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.Comment: LATEX,21 pages,submitted to Physica Script

P.A.M. Dirac and the Discovery of Quantum Mechanics

Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described