275 research outputs found
Is there a relativistic nonlinear generalization of quantum mechanics?
Yes, there is. - A new kind of gauge theory is introduced, where the minimal
coupling and corresponding covariant derivatives are defined in the space of
functions pertaining to the functional Schroedinger picture of a given field
theory. While, for simplicity, we study the example of an U(1) symmetry, this
kind of gauge theory can accommodate other symmetries as well. We consider the
resulting relativistic nonlinear extension of quantum mechanics and show that
it incorporates gravity in the (0+1)-dimensional limit, where it leads to the
Schroedinger-Newton equations. Gravity is encoded here into a universal
nonlinear extension of quantum theory. The probabilistic interpretation, i.e.
Born's rule, holds provided the underlying model has only dimensionless
parameters.Comment: 10 pages; talk at DICE 2006 (Piombino, September 11-15, 2006); to
appear in Journal of Physics: Conference Series (2007
Quantum fields, cosmological constant and symmetry doubling
Energy-parity has been introduced by Kaplan and Sundrum as a protective
symmetry that suppresses matter contributions to the cosmological constant
[KS05]. It is shown here that this symmetry, schematically Energy --> - Energy,
arises in the Hilbert space representation of the classical phase space
dynamics of matter. Consistently with energy-parity and gauge symmetry, we
generalize the Liouville operator and allow a varying gauge coupling, as in
"varying alpha" or dilaton models. In this model, classical matter fields can
dynamically turn into quantum fields (Schroedinger picture), accompanied by a
gauge symmetry change -- presently, U(1) --> U(1) x U(1). The transition
between classical ensemble theory and quantum field theory is governed by the
varying coupling, in terms of a one-parameter deformation of either limit.
These corrections introduce diffusion and dissipation, leading to decoherence.Comment: Replaced by published version, no change in contents - Int. J. Theor.
Phys. (2007
General linear dynamics - quantum, classical or hybrid
We describe our recent proposal of a path integral formulation of classical
Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics,
which concerns the direct coupling of classical and quantum mechanical degrees
of freedom. This is of practical as well as of foundational interest and no
fully satisfactory solution of this problem has been established to date.
Related aspects will be observed in a general linear ensemble theory, which
comprises classical and quantum dynamics in the form of Liouville and von
Neumann equations, respectively, as special cases. Considering the simplest
object characterized by a two-dimensional state-space, we illustrate how
quantum mechanics is special in several respects among possible linear
generalizations.Comment: 17 pages; based on invited talks at the conferences DICE2010
(Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field Theory and
Gravity (Regensburg, Germany, Sept 28 - Oct 1, 2010
Experimental tests of hidden variable theories from dBB to Stochastic Electrodynamics
In this paper we present some of our experimental results on testing hidden
variable theories, which range from Bell inequalities measurements to a
conclusive test of stochastic electrodynamics
Isospin Fluctuations from a Thermally Equilibrated Hadron Gas
Partition functions, multiplicity distributions, and isospin fluctuations are
calculated for canonical ensembles in which additive quantum numbers as well as
total isospin are strictly conserved. When properly accounting for
Bose-Einstein symmetrization, the multiplicity distributions of neutral pions
in a pion gas are significantly broader as compared to the non-degenerate case.
Inclusion of resonances compensates for this broadening effect. Recursion
relations are derived which allow calculation of exact results with modest
computer time.Comment: 10 pages, 5 figure
Superselection from canonical constraints
The evolution of both quantum and classical ensembles may be described via
the probability density P on configuration space, its canonical conjugate S,
and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is,
of course, equivalent to the Schroedinger equation for the wavefunction, which
is linear. However, quite simple constraints on the canonical fields P and S
correspond to_nonlinear_ constraints on the wavefunction. Such constraints act
to prevent certain superpositions of wavefunctions from being realised, leading
to superselection-type rules. Examples leading to superselection for energy,
spin-direction and `classicality' are given. The canonical formulation of the
equations of motion, in terms of a probability density and its conjugate,
provides a universal language for describing classical and quantum ensembles on
both continuous and discrete configuration spaces, and is briefly reviewed in
an appendix.Comment: MiKTex 2.3, no figures, minor clarifications, to appear in J. Phys.
Transport equation for the photon Wigner operator in non-commutative QED
We derive an exact quantum equation of motion for the photon Wigner operator
in non-commutative QED, which is gauge covariant. In the classical
approximation, this reduces to a simple transport equation which describes the
hard thermal effects in this theory. As an example of the effectiveness of this
method we show that, to leading order, this equation generates in a direct way
the Green amplitudes calculated perturbatively in quantum field theory at high
temperature.Comment: 13 pages, twocolumn revtex4 styl
Smoothed Particle Hydrodynamics for Relativistic Heavy Ion Collisions
The method of smoothed particle hydrodynamics (SPH) is developped
appropriately for the study of relativistic heavy ion collision processes. In
order to describe the flow of a high energy but low baryon number density
fluid, the entropy is taken as the SPH base. We formulate the method in terms
of the variational principle. Several examples show that the method is very
promising for the study of hadronic flow in RHIC physics.Comment: 14 pages, 8figure
Kinetic Equation for Gluons in the Background Gauge of QCD
We derive the quantum kinetic equation for a pure gluon plasma, applying the
background field and closed-time-path method. The derivation is more general
and transparent than earlier works. A term in the equation is found which, as
in the classical case, corresponds to the color charge precession for partons
moving in the gauge field.Comment: RevTex 4, 4 pages, no figure, PRL accepted versio
Hydrodynamical instabilities in an expanding quark gluon plasma
We study the mechanism responsible for the onset of instabilities in a chiral
phase transition at nonzero temperature and baryon chemical potential. As a
low-energy effective model, we consider an expanding relativistic plasma of
quarks coupled to a chiral field, and obtain a phenomenological chiral
hydrodynamics from a variational principle. Studying the dispersion relation
for small fluctuations around equilibrium, we identify the role played by
chiral waves and pressure waves in the generation of instabilities. We show
that pressure modes become unstable earlier than chiral modes.Comment: 7 pages, 4 figure
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