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

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

Non-perturbative Unitarity of Gravitational Higgs Mechanism

In this paper we discuss massive gravity in Minkowski space via gravitational Higgs mechanism, which provides a non-perturbative definition thereof. Using this non-perturbative definition, we address the issue of unitarity by studying the full nonlinear Hamiltonian for the relevant metric degrees of freedom. While perturbatively unitarity is not evident, we argue that no negative norm state is present in the full nonlinear theory.Comment: 15 pages, Phys. Rev. D versio

Neutrino Masses and Mixing, Quark-lepton Symmetry and Strong Right-handed Neutrino Hierarchy

Assuming the same form of all mass matrices as motivated by quark-lepton symmetry, we discuss conditions under which bi-large mixing in the lepton sector can be obtained with a minimal amount of fine tuning requirements for possible models. We assume hierarchical mass matrices, dominated by the 3-3 element, with off-diagonal elements much smaller than the larger neighboring diagonal element. Characteristic features of this scenario are strong hierarchy in masses of right-handed neutrinos, and comparable contributions of both lighter right-handed neutrinos to the resulting left-handed neutrino Majorana mass matrix. Due to obvious quark lepton symmetry, this approach can be embedded into grand unified theories. The mass of the lightest neutrino does not depend on details of a model in the leading order. The right-handed neutrino scale can be identified with the GUT scale in which case the mass of the lightest neutrino is given as (m_{top}^2/M_{GUT}) |U_{\tau 1}|^2.Comment: 7 page

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

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there exists an ongoing controversy whether the notion of the maximum entropy principle can be extended in a meaningful way to non-extensive, non-ergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for non-ergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.Comment: 6 pages, 1 figure. To appear in PNA