Initial states and decoherence of histories

We study decoherence properties of arbitrarily long histories constructed from a fixed projective partition of a finite dimensional Hilbert space. We show that decoherence of such histories for all initial states that are naturally induced by the projective partition implies decoherence for arbitrary initial states. In addition we generalize the simple necessary decoherence condition [Scherer et al., Phys. Lett. A (2004)] for such histories to the case of arbitrary coarse-graining.Comment: 10 page

Causality in Time-Neutral Cosmologies

Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signalling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be transmitted with probability arbitrarily close to one by the use of redundant signals. However, the outcome probabilities of quantum measurements generally depend on precisely which past {\it and future} measurements take place. As the transmission of any signal relies on quantum measurements, its transmission probability is similarly context-dependent. As a result, the standard superluminal signalling paradoxes do not apply. Despite their unusual features, the models are internally consistent. These results illustrate an interesting conceptual point. The standard view of Minkowski causality is not an absolutely indispensable part of the mathematical formalism of relativistic quantum theory. It is contingent on the empirical observation that naturally occurring ensembles can be naturally pre-selected but not post-selected.Comment: 5 pages, RevTeX. Published version -- minor typos correcte

Quasiclassical Coarse Graining and Thermodynamic Entropy

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th birthday, minor correction

Path Integral Solution by Sum Over Perturbation Series

A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method. Different from the earlier treatment based on the space-time transformation and infinite multiple-valued trasformation of Kustaanheimo-Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simple Green's function and an explicit path integral is avoided.Comment: 13 pages, ReVTeX, no figure

Enhanced Tau Lepton Signatures at LHC in Constrained Supersymmetric Seesaw

We discuss the possible enhancement of the tau lepton events at LHC when the left-handed stau doublet becomes light (which can be even lighter than the right-handed stau). This is illustrated in the constrained supersymmetric seesaw model where the slepton doublet mass is suppressed by the effects of a large neutrino Yukawa coupling. We study a few representative parameter sets in the sneutrino coannihilation regions where the tau sneutrino is NLSP and the stau coannihilation regions where the stau is NLSP both of which yield the thermal neutralino LSP abundance determined by WMAP.Comment: 15 pages, 3 figures, references adde

Quasiclassical Equations of Motion for Nonlinear Brownian Systems

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros

Verifiable Radiative Seesaw Mechanism of Neutrino Mass and Dark Matter

A minimal extension of the Standard Model is proposed, where the observed left-handed neutrinos obtain naturally small Majorana masses from a one-loop radiative seesaw mechanism. This model has two candidates (one bosonic and one fermionic) for the dark matter of the Universe. It has a very simple structure and should be verifiable in forthcoming experiments at the Large Hadron Collider.Comment: 8 pages, 1 figur

Connection Between the Neutrino Seesaw Mechanism and Properties of the Majorana Neutrino Mass Matrix

If it can be ascertained experimentally that the 3X3 Majorana neutrino mass matrix M_nu has vanishing determinants for one or more of its 2X2 submatrices, it may be interpreted as supporting evidence for the theoretically well-known canonical seesaw mechanism. I show how these two things are connected and offer a realistic M_nu with two zero subdeterminants as an example.Comment: title changed, version to appear in PRD(RC

Gauge Invariance of the Muonium-Antimuonium Oscillation Time Scale and Limits on Right-Handed Neutrino Masses

The gauge invariance of the muonium-antimuonium ($M\bar{M}$) oscillation time scale is explicitly demonstrated in the Standard Model modified only by the inclusion of singlet right-handed neutrinos and allowing for general renormalizable interactions. The see-saw mechanism is exploited resulting in three light Majorana neutrinos and three heavy Majorana neutrinos with mass scale $M_R\gg M_W$. The leading order matrix element contribution to the $M\bar{M}$ oscillation process is computed in $R_\xi$ gauge and shown to be $\xi$ independent thereby establishing the gauge invariance to this order. Present experimental limits resulting from the non-observation of the oscillation process sets a lower limit on $M_R$ roughly of order 600 GeV.Comment: 17 pages, 6 figures, Late