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

A simple necessary decoherence condition for a set of histories

Within the decoherent histories formulation of quantum mechanics, we investigate necessary conditions for decoherence of arbitrarily long histories. We prove that fine-grained histories of arbitrary length decohere for all classical initial states if and only if the unitary evolution preserves classicality of states (using a natural formal definition of classicality). We give a counterexample showing that this equivalence does not hold for coarse-grained histories.Comment: 11 pages,LaTe

Singular Instantons Made Regular

The singularity present in cosmological instantons of the Hawking-Turok type is resolved by a conformal transformation, where the conformal factor has a linear zero of codimension one. We show that if the underlying regular manifold is taken to have the topology of $RP^4$, and the conformal factor is taken to be a twisted field so that the zero is enforced, then one obtains a one-parameter family of solutions of the classical field equations, where the minimal action solution has the conformal zero located on a minimal volume noncontractible $RP^3$ submanifold. For instantons with two singularities, the corresponding topology is that of a cylinder $S^3\times [0,1]$ with D=4 analogues of `cross-caps' at each of the endpoints.Comment: 23 pages, compressed and RevTex file, including nine postscript figure files. Submitted versio

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

The U(1) symmetry of the non-tribimaximal pattern in the degenerate mass spectrum case of the neutrino mass matrix

On account of the new neutrino oscillation data signalling a non-zero value for the smallest mixing angle ($\theta_z$), we present an explicit realization of the underlying U(1) symmetry characterizing the maximal atmospheric mixing angle ($\theta_y = \pi / 4$) pattern with two degenerate masses but now with generic values of $\theta_z$. We study the effects of the form invariance with respect to U(1), and/or $Z_3$, $Z_2$ subgroups, on the Yukawa couplings and the mass terms. Later on, we specify $\theta_z$ to its experimental best fit value ($\sim 8^o$), and impose the symmetry in an entire model which includes charged leptons, and many Higgs doublets or standard model singlet heavy scalars, to show that it can make room for the charged lepton mass hierarchies. In addition, we show for the non-tribimaximal value of $\theta_z \neq 0$ within type-I seesaw mechanism enhanced with flavor symmetry that neutrino mass hierarchies can be generated. Furthermore, lepton/baryogenesis can be interpreted via type-II seesaw mechanism within a setup meeting the flavor U(1)-symmetry.Comment: latex, 1 table, 20 pages. Typos are corrected, shortened version to appear in Phys. Rev.

Light Scalar Mesons as Manifestation of Spontaneously Broken Chiral Symmetry

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the \sigma(600) meson. We show that the kaon loop mechanism of the \phi radiative decays, ratified by experiment, points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor q\bar q mesons that are produced via two-quark transitions $\gamma\gamma\to q\bar q$. The history of spontaneous breaking of symmetry in quantum physics is discussed in Appendix.Comment: Talk at The International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" devoted to the 100th anniversary of N.N.Bogolyubov's birth that was held from August 21 to August 22,2009 in Moscow at the Russian Academy of Sciences (RAS) and from August 23 to August 27, 2009 in Dubna at the Joint Institute for Nuclear Research (JINR

Running with Triplets: How Slepton Masses Change With Doubly-Charged Higgses

We examine the slepton masses of SUSYLR models and how they change due the presence of light-doubly charged higgs bosons. We discover that the measurement of the slepton masses could bound and even predict the value of the third generation Yukawa coupling of leptons to the SU(2)_R Triplets. We also consider the unification prospects for this model with the addition of left-handed, B - L = 0 triplets--a model we call the Triplet Extended Supersymmetric Standard Model (TESSM). Finally, we discuss the changes in the slepton masses due to the presence of the SU(2)_L triplets.Comment: 20 pages, 6 figures, 4 table

Neutrino Mixing Predictions of a Minimal SO(10) Model with Suppressed Proton Decay

During the past year, a minimal renormalizable supersymmetric SO(10) model has been proposed with the following properties: it predicts a naturally stable dark matter and neutrino mixing angles theta_atm and theta_13 while at the same time accommodating CKM CP violation among quarks with no SUSY CP problem. Suppression of proton decay for all allowed values of tan beta strongly restricts the flavor structure of the model making it predictive for other processes as well. We discuss the following predictions of the model in this paper, e.g. down-type quark masses, and neutrino oscillation parameters, U_e3, delta_MNSP, which will be tested by long baseline experiments such as T2K and subsequent experiments using the neutrino beam from JPARC. We also calculate lepton flavor violation and the lepton asymmetry of the Universe in this model.Comment: 22 pages, 11 figure

Intermediate left-right gauge symmetry, unification of couplings and fermion masses in SUSY SO(10)×S4SO(10)\times S_4

If left-right gauge theory occurs as an intermediate symmetry in a GUT then, apart from other advantages, it is possible to obtain the see-saw scale necessary to understand small neutrino masses with Majorana coupling of order unity. Barring threshold or non-renormalizable gravitational effects, or assumed presence of additional light scalar particles of unprescribed origin, all other attempts to achieve manifest one-loop gauge coupling unification in SUSY SO(10) with left-right intermediate symmetry have not been successful so far. Attributing this failure to lack of flavor symmetry in the GUT, we show how the spontaneous symmetry breaking of $SO(10)\times S_4$ leads to such intermediate scale extending over a wide range, $M_R \simeq 5\times 10^{9}$ GeV to $10^{15}$ GeV. All the charged fermion masses are fitted at the see-saw scale, $M_N\simeq M_R \simeq 4 \times 10^{13}$ GeV which is obtained with Majorana coupling $f_0 \simeq 1$. Using a constrained parametrization in which CP-violation originates only from quark sector, besides other predictions made in the neutrino sector, the reactor mixing angle is found to be $\theta_{13} \simeq 3^{\circ} - 5^{\circ}$ which is in the range accessible to ongoing and planned experiments. The leptonic Dirac phase turns out to be $\delta \sim 2.9- 3.1$ radians with Jarlskog invariant $J \sim 2.95 \times 10^{-5} - 10^{-3}$.Comment: Minor clarification and few references added to match the published versio

Decoherence Functional and Probability Interpretation

We confirm that the diagonal elements of the Gell-Mann and Hartle's decoherence decoherence functional are equal to the relative frequencies of the results of many identical experiments, when a set of alternative histories decoheres. We consider both cases of the pure and mixed initial states.Comment: 9 pages, UCSBTH-92-40 and MMC-M-