Quantum Coherence and Closed Timelike Curves

Various calculations of the $S$ matrix have shown that it seems to be non unitary for interacting fields when there are closed timelike curves. It is argued that this is because there is loss of quantum coherence caused by the fact that part of the quantum state circulates on the closed timelike curves and is not measured at infinity. A prescription is given for calculating the superscattering matrix $\$$ on space times whose parameters can be analytically continued to obtain a Euclidean metric. It is illustrated by a discussion of a spacetime in with two disks in flat space are identified. If the disks have an imaginary time separation, this corresponds to a heat bath. An external field interacting with the heat bath will lose quantum coherence. One can then analytically continue to an almost real separation of the disks. This will give closed timelike curves but one will still get loss of quantum coherence.Comment: 13 page

A proof of factorization for B -> D pi

We prove that the matrix elements of four fermion operators mediating the decay B^0 -> D^+ \pi^- and B^- -> D^0 \pi^- factor into the product of a form factor describing the B -> D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha_s, up to corrections suppressed by factors of 1/mb, 1/mc, and 1/E_pi. It is not necessary to assume that the pion state is dominated by the q-qbar Fock state.Comment: 4 pages, 3 figs, PRL versio

Quantum Computational Complexity in the Presence of Closed Timelike Curves

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.Comment: 8 pages, 2 figures. Minor changes and typos fixed. Reference adde

Selection rules in three-body B decay from factorization

Extending the dynamics underlying the factorization calculation of two-body decays, we propose simple selection rules for nonresonant three-body B decays. We predict, for instance, that in the Dalitz plot of B^0-->D^0-bar\pi^+\pi^-, practically no events should be found in the corner of E(\pi^+) < \Lambda_{QCD} as compared with the corner of E(\pi^-) < \Lambda_{QCD}. We also predict that there should be very few three-body decay events with a soft meson resonance and two energetic mesons or meson resonances. The selection rules are quite different from the soft pion theorem, since they apply to different kinematical regions. For B^0 -->D^0-bar\pi^+\pi^-, the latter predicts that the decay matrix element vanishes in the zero-four-momentum limit of \pi^+ instead of \pi^-. Since this marked difference from the soft pion theorem is directly related to the issue of short-distance QCD dominance in the FSI of two-body B decays, experimental test of the selection rules will shed light on strong interaction dynamics of B decay.Comment: 12 pages in REVTEX including 3 eps figure

Isospin Multiplet Structure in Ultra--Heavy Fermion Bound States

The coupled Bethe--Salpeter bound state equations for a $Q\bar Q$ system, where $Q=(U,D)$ is a degenerate, fourth generation, super--heavy quark doublet, are solved in several ladder approximation models. The exchanges of gluon, Higgs and Goldstone modes in the standard model are calculated in the ultra--heavy quark limit where weak $\gamma, W^\pm$ and $Z^0$ contributions are negligible. A natural $I=0$ and $I=1$ multiplet pattern is found, with large splittings occuring between the different weak iso--spin states when $M_Q$, the quark masses, are larger than values in the range $0.4 TeV<M_Q<0.8 TeV$, depending on which model is used. Consideration of ultra--heavy quark lifetime constraints and $U-D$ mass splitting constraints are reviewed to establish the plausibility of lifetime and mass degeneracy requirements assumed for this paper.Comment: 20 pages, 7 figures (hard copy available upon request), report# KU-HEP-93-2

Gas of wormholes: a possible ground state of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a ``gas'' of wormholes of mass m_p, the Planck mass (m_p ~= 10^{19}GeV) and average distance l_p, the Planck length a_p(a_p ~= 10^{-33}cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l_p, the Planck lattice.Comment: 56 pages, revised version to appear in General Relativity and Gravitation (2000

Heavy Mesons in Two Dimensions

The large mass limit of QCD uncovers symmetries that are not present in the QCD lagrangian. These symmetries have been applied to physical (finite mass) systems, such as B and D mesons. We explore the validity of this approximation in the 't Hooft model (two-dimensional QCD in the large-N approximation). We find that the large mass approximation is good, even at the charm mass, for form factors, but it breaks down for the pseudoscalar decay constant.Comment: 4 pages, 3 figures inc

Simple Quantum Systems in Spacetimes with Closed Timelike Curves

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with hard spheres and the exact solution of a totally discrete model are unitary.Comment: 15 pages, CALT-68-180

Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics

We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events bewcome certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the "many worlds interpretation". We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.Comment: no figure