Unitarity Restoration in the Presence of Closed Timelike Curves

A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations, this proposal is causal, linear in the initial density matrix and preserves probability. It provides a physically reasonable interpretation of invertible nonunitary evolution by redefining the final Hilbert space so that the evolution is unitary or equivalently by removing the nonunitary part of the evolution operator using a polar decomposition.Comment: LaTeX, 17pp, Revisions: Title change, expanded and clarified presentation of original proposal, esp. with regard to Heisenberg picture and remaining in original Hilbert spac

Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such non-unitarity. The usual notion of state on a spacelike surface is lost in this generalization and familiar notions of causality are modified. There is no signaling outside the light cone, no non-conservation of energy, no ``Everett phones'', and probabilities of present events do not depend on particular alternatives of the future. However, the generalization is acausal in the sense that the existence of non-chronal regions of spacetime in the future can affect the probabilities of alternatives today. The detectability of non-unitary evolution and violations of causality in measurement situations are briefly considered. The evolution of information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0

Palatini Variational Principle for an Extended Einstein-Hilbert Action

We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.Comment: 14 pages, LaTe

Spacetime Information

In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have a notion of state on a spacelike surface. It must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering histories it may display. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse- grainings of sum-over-histories quantum mechanics. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with non-unitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ``evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics.Comment: 47pages, 2 figures, UCSBTH 94-0

Supersymmetric SO(10) for fermion masses and mixings: rank-1 structures of flavour

We consider a supersymmetric SO(10) model with a SU(3) symmetry of flavour in which fermion masses emerge via the see-saw mixing with superheavy fermions in 16+16bar representations. In this model the dangerous D=5 operators of proton decay are naturally suppressed and flavour-changing supersymmetric effects are under control. The mass matrices for all fermion types (up and down quarks, charged leptons as well as neutrinos) appear in the form of combinations of three rank-1 matrices, common to all types of fermions, with different coefficients that are successive powers of small parameters, related to each other by SO(10) symmetry properties. Two versions of the model are considered, in which approximate grand unification of masses takes place between quarks and leptons of the first family (with very small \tan\beta) or for the ones of the second family (predicting moderate \tan\beta ~ 7-8). The second version exhibits an interesting mechanism of unification of the determinants of the Yukawa matrices of all types of fermions at the GUT scale and it provides a perfect fit of the known data for fermion masses, mixing and CP-violation. It predicts a hierarchical pattern of neutrino masses with non-zero theta_e3, within 2-7 degrees. In addition, it predicts the correct sign of the baryon asymmetry of the Universe via the leptogenesys scenario.Comment: 30 Pages, 3 figures. Clarified comments on neutrino scales and on universal seesaw, updated references. Version appeared on JHE

Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models

A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with the time is also discussed.Comment: 23 pages, accepted in PR

A Little Higgs model of neutrino masses

Little Higgs models are formulated as effective theories with a cut-off of up to 100 times the electroweak scale. Neutrino masses are then a puzzle, since the usual see-saw mechanism involves a much higher scale that would introduce quadratic corrections to the Higgs mass parameter. We propose a model that can naturally accommodate the observed neutrino masses and mixings in Little Higgs scenarios. Our framework does not involve any large scale or suppressed Yukawa couplings, and it implies the presence of three extra (Dirac) neutrinos at the TeV scale. The masses of the light neutrinos are induced radiatively, they are proportional to small (\approx keV) mass parameters that break lepton number and are suppressed by the Little Higgs cut-off.Comment: 10 pages, 3 figure

Interactions between Simulant Vitrified Nuclear Wastes and high pH solutions: A Natural Analogue Approach

This study details the characterization of a glass sample exposed to hyperalkaline water and calcium-rich sediment for an extended time period (estimated as 2-70 years) at a lime (CaO) waste site in the UK. We introduce this site, known as Peak Dale, in reference to its use as a natural analogue for nuclear waste glass dissolution in the high pH environment of a cementitious engineered barrier of a geological disposal facility. In particular, a preliminary assessment of alteration layer chemistry and morphology is described and the initiation of a long-term durability assessment is outlined

Supersymmetry for Fermion Masses

It is proposed that supersymmetry (SUSY) maybe used to understand fermion mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic symmetry among the three generation SU(2) doublets. SUSY breaks at a high energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is unnaturally small. No additional global symmetry, like the R-parity, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values which are about (10^0-10^{-2}). Under the family symmetry, only the third generation charged fermions get their masses. This family symmetry is broken in the soft SUSY breaking terms which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the tau mass is from the Higgs vacuum expectation value (VEV) and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both Z_{3L} and SUSY breaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. |V_{e3}| which is for nu_e-nu_{tau} mixing is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains m_c/m_s, m_s/m_e, m_d > m_u and so on. Other aspects of the model are discussed.Comment: 25 pages, 3 figures, revtex4; neutrino oscillation and many discussions added, smallness of the electron mass due to supersymmetry pointed out; v3: numerical errors correcte