No Eigenvalue in Finite Quantum Electrodynamics

We re-examine Quantum Electrodynamics (QED) with massless electron as a finite quantum field theory as advocated by Gell-Mann-Low, Baker-Johnson, Adler, Jackiw and others. We analyze the Dyson-Schwinger equation satisfied by the massless electron in finite QED and conclude that the theory admits no nontrivial eigenvalue for the fine structure constant.Comment: 13 pages, Late

Algebraic and geometric aspects of generalized quantum dynamics

\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and ordinary symplectic structure.Comment: 10pages,revtex, IASSNSHEP-93/5

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the position operator for the center of mass of the mirror, and \rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the CSL model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10^{8}. Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.Comment: 4 pages, RevTeX. Substantial changes mad

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.Comment: 13 pages, LaTeX, 3 figure

On Di\'osi-Penrose criterion of gravity-induced quantum collapse

It is shown that the Di\'osi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of space-time, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of space-time may result in rapider collapse of the superposition of energy eigenstates than required by the Di\'osi-Penrose criterion.Comment: 5 pages, no figure

The frictional Schr\"odinger-Newton equation in models of wave function collapse

Replacing the Newtonian coupling G by -iG, the Schrodinger-Newton equation becomes ``frictional''. Instead of the reversible Schrodinger-Newton equation, we advocate its frictional version to generate the set of pointer states for macroscopic quantum bodies.Comment: 6pp LaTeX for J.Phys.Conf.Ser.+2 figs. Talk given at the Int. Workshop DICE2006 "Quantum Mechanics between Decoherence and Determinism: new aspects from particle physics to cosmology" Piombino, Sept 11-15, 200

Collapse models with non-white noises II: particle-density coupled noises

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schr\"odinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision

Collapse models with non-white noises

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrodinger terms of the equation induce the collapse of the wave function to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the ``imaginary'' noise trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J. Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509

Comments on Proposed Gravitational Modifications of Schrodinger Dynamics and their Experimental Implications

We discuss aspects of gravitational modifications of Schrodinger dynamics proposed by Diosi and Penrose. We consider first the Diosi-Penrose criterion for gravitationally induced state vector reduction, and compute the reduction time expected for a superposition of a uniform density cubical solid in two positions displaced by a small fraction of the cube side. We show that the predicted effect is much smaller than would be observable in the proposed Marshall et al. mirror experiment. We then consider the ``Schrodinger -Newton'' equation for an N-particle system. We show that in the independent particle approximation, it differs from the usual Hartree approximation applied to the Newtonian potential by self-interaction terms, which do not have a consistent Born rule interpretation. This raises doubts about the use of the Schrodinger-Newton equation to calculate gravitational effects on molecular interference experiments. When the effects of Newtonian gravitation on molecular diffraction are calculated using the standard many-body Schrodinger equation, no washing out of the interference pattern is predicted.Comment: Tex, 17