Arrow of time in a recollapsing quantum universe

We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects in the region of the classical turning point. Since gravitational time dilation diverges at horizons, collapsing matter must then start re-expanding ``anticausally" (controlled by the reversed arrow) before horizons or singularities can form. We also discuss the meaning of the time-asymmetric expression used in the definition of ``consistent histories". We finally emphasize that there is no mass inflation nor any information loss paradox in this scenario.Comment: Many conceptual clarifications include

Unitarity of Quantum Theory and Closed Time-Like Curves

Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the inner product on the final Hilbert space. We give a rigorous description of this proposal and note an operational problem which arises when one considers the composition of two or more non-unitary evolutions. We propose an alternative method by which unitarity of the evolution may be regained, by extending $X$ to a unitary evolution on a larger (possibly indefinite) inner product space. The proposal removes the ambiguity noted by Jacobson in assigning expectation values to observables localised in regions spacelike separated from the CTC region. We comment on the physical significance of the possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D. Some changes are made to expand our discussion of Anderson's Proposal for restoring unitarit

Perturbative two- and three-loop coefficients from large beta Monte Carlo

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large beta on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z_3 tunneling.Comment: 6 pages, 5 figures. Contributions of Howard Trottier and Paul Mackenzie to Lattice '9

Scaling of the B and D meson spectrum in lattice QCD

We give results for the $B$ and the $D$ meson spectrum using NRQCD on the lattice in the quenched approximation. The masses of radially and orbitally excited states are calculated as well as $S$-wave hyperfine and $P$-wave fine structure. Radially excited $P$-states are observed for the first time. Radial and orbital excitation energies match well to experiment, as does the strange-non-strange $S$-wave splitting. We compare the light and heavy quark mass dependence of various splittings to experiment. Our $B$-results cover a range in lattice spacings of more than a factor of two. Our $D$-results are from a single lattice spacing and we compare them to numbers in the literature from finer lattices using other methods. We see no significant dependence of physical results on the lattice spacing. PACS: 11.15.Ha 12.38.Gc 14.40.Lb 14.40.NdComment: 78 pages, 29 tables, 30 figures Revised version. Minor corrections to spelling and wordin

Hybrid configuration content of heavy S-wave mesons

We use the non-relativistic expansion of QCD (NRQCD) on the lattice to study the lowest hybrid configuration contribution to the ground state of heavy S-wave mesons. Using lowest-order lattice NRQCD to create the heavy-quark propagators, we form a basis of ``unperturbed'' S-wave and hybrid states. We then apply the lowest-order coupling of the quark spin and chromomagnetic field at an intermediate time slice to create ``mixed'' correlators between the S-wave and hybrid states. From the resulting amplitudes, we extract the off-diagonal element of our two-state Hamiltonian. Diagonalizing this Hamiltonian gives us the admixture of hybrid configuration within the meson ground state. The present effort represents a continuation of previous work: the analysis has been extended to include lattices of varying spacings, source operators having better overlap with the ground states, and the pseudoscalar (along with the vector) channel. Results are presented for bottomonium ($\Upsilon$, $\eta_b^{}$) using three different sets of quenched lattices. We also show results for charmonium ($J/\psi$, $\eta_c^{}$) from one lattice set, although we note that the non-relativistic approximation is not expected to be very good in this case.Comment: 9 pages, 7 figures, version to appear in Phys Rev

One-Loop Matching of the Heavy-Light A_0 and V_0 Currents with NRQCD Heavy and Improved Naive Light Quarks

One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of dimension 4 O(1/M) and O(a) operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. As part of the matching procedure we also present results for the NRQCD self energy and for massless Asqtad quark wavefunction renormalization with improved glue.Comment: 25 pages, 3 eps-figure

Adjoint "quarks" on coarse anisotropic lattices: Implications for string breaking in full QCD

A detailed study is made of four dimensional SU(2) gauge theory with static adjoint ``quarks'' in the context of string breaking. A tadpole-improved action is used to do simulations on lattices with coarse spatial spacings $a_s$, allowing the static potential to be probed at large separations at a dramatically reduced computational cost. Highly anisotropic lattices are used, with fine temporal spacings $a_t$, in order to assess the behavior of the time-dependent effective potentials. The lattice spacings are determined from the potentials for quarks in the fundamental representation. Simulations of the Wilson loop in the adjoint representation are done, and the energies of magnetic and electric ``gluelumps'' (adjoint quark-gluon bound states) are calculated, which set the energy scale for string breaking. Correlators of gauge-fixed static quark propagators, without a connecting string of spatial links, are analyzed. Correlation functions of gluelump pairs are also considered; similar correlators have recently been proposed for observing string breaking in full QCD and other models. A thorough discussion of the relevance of Wilson loops over other operators for studies of string breaking is presented, using the simulation results presented here to support a number of new arguments.Comment: 22 pages, 14 figure

Physics in the Real Universe: Time and Spacetime

The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible microphysical laws and does not represent macro-physical behaviour and the development of emergent complex systems, including life, which do indeed exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world linesComment: 28 pages, including 9 Figures. Major revision in response to referee comment

Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories

We calculate the mean link in Landau gauge for Wilson and improved SU(3) anisotropic gauge actions, using two loop perturbation theory and Monte Carlo simulation employing an accelerated Langevin algorithm. Twisted boundary conditions are employed, with a twist in all four lattice directions considerably improving the (Fourier accelerated) convergence to an improved lattice Landau gauge. Two loop perturbation theory is seen to predict the mean link extremely well even into the region of commonly simulated gauge couplings and so can be used remove the need for numerical tuning of self-consistent tadpole improvement factors. A three loop perturbative coefficient is inferred from the simulations and is found to be small. We show that finite size effects are small and argue likewise for (lattice) Gribov copies and double Dirac sheets.Comment: 13 pages of revtex

Leptonic decay constants f_Ds and f_D in three flavor lattice QCD

We determine the leptonic decay constants in three flavor unquenched lattice QCD. We use O(a^2)-improved staggered light quarks and O(a)-improved charm quarks in the Fermilab heavy quark formalism. Our preliminary results, based upon an analysis at a single lattice spacing, are f_Ds = 263(+5-9)(+/-24) MeV and f_D = 225(+11-13)(+/-21) MeV. In each case, the first reported error is statistical while the is the combined systematic uncertainty.Comment: Talk presented at Lattice2004(heavy), Fermilab, June 21-26, 2004. 3 pages, 2 figure