It is generally known that linear (free) field theories are one of the few quantum field theories that are exactly soluble. In the Schrödinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic spacetimes and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schrödinger representation in the general case. It is shown that, in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out.

We show that NS’s with large toroidal B fields tend naturally to evolve into potent gravitational-wave (GW) emitters. The toroidal field $B_t$ tends to distort the NS into a prolate shape, and this magnetic distortion dominates over the oblateness “frozen into” the NS crust for $B_t\gtrsim 3.4\times {10}^{12}\mathrm{G}({\nu }_s/300\mathrm{}\mathrm{Hz}{)}^2.$ An elastic NS with frozen-in B field of this magnitude is clearly secularly unstable: the wobble angle between the NS’s angular momentum $J^i$ and the star’s magnetic axis $n_B^i$ grows on a dissipation time scale until $J^i$ and $n_B^i$ are orthogonal. This final orientation is clearly the optimal one for GW emission. The basic cause of the instability is quite general, so we conjecture that the same final state is reached for a realistic NS, with superfluid core. Assuming this, we show that for LMXB’s with $B_t\sim 2\times {10}^{12}-2\times {10}^{14}\mathrm{G},$ the spindown from GW’s is sufficient to balance the accretion torque—supporting a suggestion by Bildsten. The spindown rates of most millisecond pulsars can also be attributed to GW emission sourced by toroidal B fields, and both these sources could be observed by LIGO II. While the first-year spindown of a newborn NS is most likely dominated by electromagnetic processes, reasonable values of $B_t$ and the (external) dipolar field $B_d$ can lead to detectable levels of GW emission, for a newborn NS in our own Galaxy.

We describe a finite-difference method for locating apparent horizons in generic spacetimes and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a $3+1$ decomposition. The result is a slicing of Kerr-Schwarzschild spacetime in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.

Reconstructed from lensing tomography, the evolution of the dark matter density field in the well-understood linear regime can provide model-independent constraints on the growth function of structure and the evolution of the dark energy density. We examine this potential in the context that high-redshift cosmology has in the future been fixed by cosmic microwave background measurements. We construct sharp tests for the existence of multiple dark matter components or a dark energy component that is not a cosmological constant. These functional constraints can be transformed into physically motivated model parameters. From the growth function, the fraction of the dark matter in a smooth component, such as a light neutrino, may be constrained to a statistical precision of $\sigma \mathrm{}\left(f\right)\mathrm{}\approx {0.0006f}_{\mathrm{sky}}^{-1/2}$ by a survey covering a fraction of sky $f_{\mathrm{sky}}$ with a redshift resolution $\Delta z=\mathrm{0.1.}\mathrm{}$ For the dark energy, a parametrization in terms of the present energy density ${\Omega }_{\mathrm{DE}},$ equation of state $w,$ and its redshift derivative $w^{\prime },$ the constraints correspond to $\sigma {\mathrm{}\left(w\right)=0.009f}_{\mathrm{sky}}^{-1/2}$ and a degenerate combination of the other two parameters. For a fixed ${\Omega }_{\mathrm{DE}},$ $\sigma {(w}^{\prime }{)=0.046f}_{\mathrm{sky}}^{-1/2}.$

In this paper, we calculate the spectrum of scalar field fluctuations in a bouncing, asymptotically flat universe, and investigate the dependence of the result on changes in the physics on length scales shorter than the Planck length which are introduced via modifications of the dispersion relation. In this model, there are no ambiguities concerning the choice of the initial vacuum state. We study an example in which the final spectrum of fluctuations depends sensitively on the modifications of the dispersion relation without needing to invoke complex frequencies. Changes in the amplitude and in the spectral index are possible, in addition to modulations of the spectrum. This strengthens the conclusions of previous work in which the spectrum of cosmological perturbations in expanding inflationary cosmologies was studied, and it was found that, for dispersion relations for which the evolution is not adiabatic, the predictions obtained for the spectrum of fluctuations are not robust towards changes in the dispersion relation.

We consider the construction of nonsingular pre-big-bang and ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is present, as is the case in the ekpyrotic scenario. This allows us to discuss the evolution of cosmological perturbations without the need to invoke matching conditions between two Einstein universes, one representing the contracting branch, the second the expanding branch. We analyze the spectra of perturbations produced during the bouncing phase and find that the spectrum of curvature fluctuations in the model proposed originally to implement the ekpyrotic scenario has a large blue tilt ${(n}_{\mathcal{R}}=3).\mathrm{}$ Except for instabilities introduced on small scales, the result agrees with what is obtained by imposing continuity of the induced metric and of the extrinsic curvature across a constant scalar field (up to $k^2$ corrections equal to the constant energy density) matching surface between the contracting and the expanding Einstein universes. We also discuss nonsingular cosmological solutions obtained when a Gauss-Bonnet term with a coefficient suitably dependent on the scalar matter field is added to the action in the Einstein frame with a potential for the scalar field present. In this scenario, nonsingular solutions are found which start in an asymptotically flat state, undergo a period of superexponential inflation, and end with a graceful exit. The spectrum of fluctuations is also calculated in this case.

The ${\pi }^0\to \gamma \gamma$ decay width is analyzed within the combined framework of chiral perturbation theory and the ${1/N}_c$ expansion up to $\mathcal{O}{(p}^6)$ and $\mathcal{O}{(p}^4\times {1/N}_c)$ in the decay amplitude. The ${\eta }^{\prime }$ is explicitly included in the analysis. It is found that the decay width is enhanced by about 4.5% due to the isospin-breaking induced mixing of the pure $U\left(3\right)\mathrm{}$ states. This effect, which is of leading order in low energy expansion, is shown to persist nearly unchanged at next to leading order. The chief prediction with its estimated uncertainty is ${\Gamma }_{{\pi }^0\to \gamma \gamma }=8.10\mathrm{}\pm 0.08\mathrm{eV}.$ This prediction at the 1% level makes the upcoming precision measurement of the decay width even more urgent. Observations on the $\eta$ and ${\eta }^{\prime }$ can also be made, especially about their mixing, which is shown to be significantly affected by next to leading order corrections.

We calculate the $6s-7s$ parity nonconserving (PNC) $E1\mathrm{}$ transition amplitude $E_{\mathrm{PNC}}$ in cesium. We use an improved all-order technique in the calculation of the correlations and include all significant contributions to $E_{\mathrm{PNC}}.$ Our final value $E_{\mathrm{PNC}}=0.904(1\mathrm{}\pm 0.5\%)\times {10}^{-11}{\mathrm{iea}}_B(-Q_W/N)$ has half the uncertainty claimed in old calculations used for the interpretation of Cs PNC experiments. The resulting nuclear weak charge $Q_W$ for Cs deviates by about $2\sigma$ from the value predicted by the standard model.

In the framework of the top-color-assisted technicolor (TC2) model, we study a neutral top-pion production process $e^{-}\overrightarrow{\gamma }{e}^{-}{\Pi }_t^0$ in this paper. Our results show that the production cross section of $e^{-}\overrightarrow{\gamma }{e}^{-}{\Pi }_t^0$ can reach the level of several tens of femtobarns, and over ${10}^3$ neutral top-pion events can be produced in the planned $e^{+}{e}^{-}$ linear colliders each year. Therefore, such a top-pion production process provides us a unique chance to detect top-pion events and test the TC2 model. On the other hand, the cross section of $e^{-}\overrightarrow{\gamma }{e}^{-}{\Pi }_t^0$ is about one order of magnitude larger than those of some similar processes in the standard model (SM) and the minimally supersymmetric standard model (MSSM) [i.e., $e^{-}\overrightarrow{\gamma }{e}^{-}H$ in the SM and $e^{-}\overrightarrow{\gamma }{e}^{-}{H}^0{(A}^0{,h}^0)$ in the MSSM]. So we can easily distinguish the neutral top-pion from other neutral Higgs bosons in the SM and MSSM.

We propose to use the different kinds of vacua of gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string states supports the ’t Hooft and Mandelstam confinement criteria. However, in the $Z_2$ gauge-Higgs model we use as a guide we find that the condensation of monopoles and center vortices is a necessary but not sufficient condition for confinement.

We extend our previous analysis of the decays $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ in the minimal supersymmetric standard model (MSSM) to include gluino and neutralino contributions. We provide analytic formulas, valid at large values of $\tan \beta ,$ for the scalar and pseudoscalar Wilson coefficients arising from neutral Higgs boson exchange diagrams with gluinos and neutralinos. Together with the remaining contributions ${(W}^{\pm },$ $H^{\pm },$ ${\tilde{\chi }}^{\pm }),$ and assuming the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be the only source of flavor violation, we assess their implications for the branching fractions $\mathcal{B}(B_{d,s}\to {\mu }^{+}{\mu }^{-}).\mathrm{}$ Of particular interest is the quantity $R\equiv \mathcal{B}(B_d\to {\mu }^{+}{\mu }^{-})/\mathcal{B}(B_s\to {\mu }^{+}{\mu }^{-}),$ since (i) the theoretical errors cancel to a large extent, and (ii) it offers a theoretically clean way of extracting the ratio $|V_{\mathrm{td}}{/V}_{\mathrm{ts}}|$ in the standard model, which predicts $R_{\mathrm{SM}}\sim |V_{\mathrm{td}}{/V}_{\mathrm{ts}}{|}^2\sim {O(10\mathrm{}}^{-2}).\mathrm{}$ Exploring three different scenarios of modified minimal flavor violation $\left(\overline{\mathrm{MFV}}\right),$ we find that part of the MSSM parameter space can accommodate large $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ branching fractions while being consistent with various experimental constraints. More importantly, we show that the ratio R can be as large as $O\left(1\right),$ while the individual branching fractions may be amenable to detection by ongoing experiments. We conclude that within the MSSM with large $\tan \beta$ the decay rates of $B_d\to {\mu }^{+}{\mu }^{-}$ and $B_s\to {\mu }^{+}{\mu }^{-}$ can be of comparable size even in the case where flavor violation is due solely to the CKM matrix.

Recent measurements of $\mathrm{CP}$ asymmetry in $\overrightarrow{B}\phi K_S$ appear to be inconsistent with standard model expectations. We explore the effect of R-parity-violating SUSY to understand the data.

We comment on the implications of the recently measured $\mathrm{CP}$ asymmetry in $\overrightarrow{B}\phi K_S$ decay. The data disfavor the standard model at $2.7\sigma$ and, if the trend persists in the future with higher statistics, require the existence of $\mathrm{CP}$ violation beyond that in the CKM matrix. In particular, the $\overrightarrow{b}s\overline{s}s$ decay amplitude would require new contributions of comparable size to the standard model ones with an order one phase. While not every model can deliver such a large amount of $\mathrm{CP}$ and flavor violation, those with substantial FCNC couplings to the Z can reproduce the experimental findings.

We present a new model for a nontopological soliton (NTS) that contains fermions, scalar particles and a gauge field. Using a variational approach, we estimate the energy of the localized configuration, showing that it can be the lowest energy state of the system for a wide range of parameters.

Recent progress in theoretical physics suggests that the dark energy in the universe might result from the rolling tachyon field of string theory. Measurements to SNe Ia can be helpful in reconstructing the equation of state of the rolling tachyon which is a possible candidate of dark energy. We present a numerical analysis for the evolution of the equation of state of the rolling tachyon and derive the reconstruction equations for the equation of state as well as the potential.

We construct light-cone gauge superstring field theory in a pp-wave background with Ramond-Ramond flux. The leading term in the interaction Hamiltonian is determined up to an overall function of $p^{+}$ by requiring closure of the pp-wave superalgebra. The bosonic and fermionic Neumann matrices for this cubic vertex are derived, as is the interaction point operator. We comment on the development of a $1/\mu p^{+}$ expansion for these results.

It is noted that a finite Penrose limit for brane probes with nonzero worldvolume fluxes does not generically exist; this is closely related to the observation by Blau and co-workers that for a brane probe the Penrose limit is equivalent to an infinite-tension limit. It is shown that when the limit exists, however, the number of supersymmetries preserved by the probe does not decrease.

We consider a class of multimatrix models with an action which is $O\left(D\right)\mathrm{}$ invariant, where D is the number of $N\times N$ Hermitian matrices $X_{\mu },$ $\mu =1,\dots ,D.\mathrm{}$ The action is a function of all the elementary symmetric functions of the matrix $T_{\mu \nu }=\mathrm{Tr}{(X}_{\mu }{X}_{\nu })/N.\mathrm{}$ We address the issue of whether the $O\left(D\right)\mathrm{}$ symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the $O\left(D\right)\mathrm{}$ symmetry is maximally broken.

The vacuum expectation values of the energy-momentum tensor are investigated for massless scalar fields satisfying Dirichlet or Neumann boundary conditions and for the electromagnetic field with perfect conductor boundary conditions on two infinite parallel plates moving by uniform proper acceleration through the Fulling-Rindler vacuum. The scalar case is considered for general values of the curvature coupling parameter and in an arbitrary number of spacetime dimensions. The mode-summation method is used with a combination of a variant of the generalized Abel-Plana formula. This allows us to extract manifestly the contributions to the expectation values due to a single boundary. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction terms. The first one contains well-known surface divergences and needs further regularization. The interaction forces between the plates are always attractive for both scalar and electromagnetic cases. An application to the “Rindler wall” is discussed.