We present results of a simulation of two flavor QCD on a ${16}^3\times 4$ lattice using p4-improved staggered fermions with bare quark mass $m/T=0.4$. Derivatives of the thermodynamic grand canonical partition function $Z(V,T,{\mu }_u,{\mu }_d)$ with respect to chemical potentials ${\mu }_{u,d}$ for different quark flavors are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of ${\mu }_q=({\mu }_u+{\mu }_d)/2$ via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergence of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.

In the calculation of the anomalous magnetic moment of $W^{\pm }$ bosons, we discuss vector anomalies occurring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regulation method, we extend the analysis using both the manifestly covariant formulation and the light-front Hamiltonian formulation with several different regularization methods. We find that the zero-mode contribution to the helicity zero-to-zero amplitude for the $W^{\pm }$ gauge bosons is crucial for the correct light-front (LF) calculations. Further, we confirm that the anomaly-free condition found in the analysis of the axial anomaly can also get rid of the vector anomaly in light-front dynamics (LFD) as well as in the manifestly covariant calculations. Our findings in this work may provide a bottom-up fitness test not only to the LF calculations but also to the theory itself, whether it is any extension of the Standard Model or an effective field theoretic model for composite systems.

The problem of reduction (wave packet reduction) is reexamined under two simple conditions: Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame of quantum field theory and the standard model. These conditions lead to an essentially unique model for reduction. Consistency with renormalization and time-reversal violation suggest however a primary action in the vicinity of Planck’s length. The inclusion of quantum gravity and the uniqueness of space time point moreover to generalized quantum theory, first proposed by Gell-Mann and Hartle, as a convenient framework for developing this model into a more complete theory.

A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken $\mathcal{P}\mathcal{T}$ (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called $\mathcal{C}$. It is shown here that $\mathcal{C}$ is the complex extension of the intrinsic parity operator and that the $\mathcal{C}$ operator transforms under the Lorentz group as a scalar.

We prove in full generality the thermal operator representation for Matsubara sums in a relativistic field theory of scalar and fermionic particles. It states that the full result of performing the Matsubara sum associated to any given Feynman graph, in the imaginary-time formalism of finite-temperature field theory, can be directly obtained from its corresponding zero-temperature energy integral, by means of a simple linear operator, which is independent of the external Euclidean energies and whose form depends solely on the topology of the graph.

We study how different types of blowups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blowups can be expected. One criteria is related to the so-called geometric blowup leading to gradient catastrophes, while the other is based upon the ODE-mechanism leading to blowups within finite time. We show how both mechanisms work in the case of a simple one-dimensional wave equation with a dynamic wave speed and sources, and later explore how those blowups can appear in one-dimensional numerical relativity. In the latter case we recover the well known “gauge shocks” associated with Bona-Massó–type slicing conditions. However, a crucial result of this study has been the identification of a second family of blowups associated with the way in which the constraints have been used to construct a hyperbolic formulation. We call these blowups “constraint shocks” and show that they are formulation specific, and that choices can be made to eliminate them or at least make them less severe.

The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz violation is investigated. Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentz-invariant theory. A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering the spontaneous Lorentz violation. The results are illustrated within the general class of bumblebee models involving vacuum values for a vector field. In Minkowski and Riemann spacetimes, the bumblebee model provides a dynamical theory generating a photon as a Nambu-Goldstone boson for spontaneous Lorentz violation. The Maxwell and Einstein-Maxwell actions are automatically recovered in axial gauge. Associated effects of potential experimental relevance include Lorentz-violating couplings in the matter and gravitational sectors of the Standard-Model Extension and unconventional Lorentz-invariant couplings. In Riemann-Cartan spacetime, the possibility also exists of a Higgs mechanism for the spin connection, leading to the absorption of the propagating Nambu-Goldstone modes into the torsion component of the gravitational field.

With the WMAP data we can now begin to test realistic models of inflation involving multiple scalar fields. These naturally lead to correlated adiabatic and isocurvature (entropy) perturbations with a running spectral index. We present the first full ($9$ parameter) likelihood analysis of double inflation with WMAP data and find that despite the extra freedom, supersymmetric hybrid potentials are strongly constrained with less than $7\%$ correlated isocurvature component allowed when standard priors are imposed on the cosomological parameters. As a result we also find that Akaike and Bayesian model selection criteria rather strongly prefer single-field inflation, just as equivalent analysis prefers a cosmological constant over dynamical dark energy in the late universe. It appears that simplicity is the best guide to our universe.

We determine the range of parameter space of an Interacting Quintessence Model that best fits the recent WMAP measurements of Cosmic Microwave Background temperature anisotropies. We only consider cosmological models with zero spatial curvature. We show that if the quintessence scalar field decays into cold dark matter at a rate that brings the ratio of matter to dark energy constant at late times, the cosmological parameters required to fit the CMB data are: dark energy density ${\Omega }_x=0.43\pm 0.12$, baryon fraction ${\Omega }_b=0.08\pm 0.01$, slope of the matter power spectrum at large scales $n_s=0.98\pm 0.02$ and Hubble constant $H_0=56\pm 4\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. The data prefers a dark energy component with a dimensionless decay rate parameter $c^2=0.005$ and noninteracting models are consistent with the data only at the $99.9\%$ confidence level. Using the Bayesian Information Criteria we show that this extra parameter fits the data better than models with no interaction. The quintessence equation of state parameter is less constrained; i.e., the data sets an upper limit $w_x\le -0.86$ at the same level of significance. When the WMAP anisotropy data are combined with supernovae data, the density parameter of dark energy increases to ${\Omega }_x\simeq 0.68$ while $c^2$ augments to $6.3\times {10}^{-3}$. Models with quintessence decaying into dark matter provide a clean explanation for the coincidence problem and are a viable cosmological model, compatible with observations of the CMB, with testable predictions. Accurate measurements of baryon fraction and/or of matter density independent of the CMB data, would support/disprove these models.

I discuss several issues that arise when trying to constrain the dark energy equation of state using correlations of the integrated Sachs-Wolfe effect with galaxy counts and lensing of the cosmic microwave background. These techniques are complementary to others such as galaxy shear surveys, and can use data that will already be obtained from currently planned observations. In regimes where cosmic variance and shot noise are the dominant sources of error, constraints could be made on the mean equation of state to $\pm 0.33$ and its first derivative to $\pm 1.0$. Perhaps more interesting is that the determination of dark energy parameters by these types of experiments depends strongly on the presence or absence of perturbations in the dark energy fluid.

We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform density curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform density and comoving curvature perturbations at second order, in a scalar field dominated universe, are conserved. Finally, in the light of this result, we comment on the variables recently used in the literature to compute non-Gaussianities.

We derive the gluon initiated contribution to the initial condition for the perturbative fragmentation function of a heavy quark through order $\mathcal{O}({\alpha }_s^2)$ in the $\overline{\mathrm{MS}}$ scheme. This result is needed for the resummation with next-to-next-to-leading logarithmic accuracy of quasicollinear logarithms ${ln}^k(m^2)$ in heavy quark differential distributions by solving the complete Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation. Together with the previously evaluated fermion initiated components, this result completes the derivation of the initial condition for the perturbative fragmentation function at next-to-next-to-leading order.

Using the Schwinger-Keldysh technique, we derive the transport equations for a system of quantum scalar fields. We first discuss the general structure of the equations and then their collision terms. Taking into account up to three-loop diagrams in ${\varphi }^3$ model and up to four-loop diagrams in ${\varphi }^4$ model, we obtain transport equations which include the contributions of multiparticle collisions and particle production processes, in addition to mean-field effects and binary interactions.

Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. In this context, we consider the hypothesis that this transition involves a quantum mechanical process. Our analysis is entirely analytical, with the objective of finding explicit mathematical expressions for the different quantum mechanical states and their cosmological implications. We employ a Friedmann-Robertson-Walker (FRW) minisuperspace model, characterized by two Lorentzian sectors, separated by a classically forbidden region. This is the configuration associated with the evolution of a generalized Chaplygin gas in a FRW universe. The Hartle-Hawking and Vilenkin wave functions are then computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, for specific initial conditions we found that the generalized Chaplygin gas parameters become related through an expression involving an integer $n$. We also introduce a phenomenological association between some brane-world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. The aim is to promote a discussion and subsequent research on the quantum creation of brane cosmologies from such a perspective. Additional results in this paper suggest that the brane tension would become related with the generalized Chaplygin gas parameters through another expression involving an integer.

The present $B\to \pi K$ data is studied in the context of the standard model (SM) and with new physics (NP). We confirm that the SM has difficulties explaining the $B\to \pi K$ measurements. By adopting an effective-lagrangian parametrization of NP effects, we are able to rule out several classes of NP. Our model-independent analysis shows that the $B\to \pi K$ data can be accommodated by NP in the electroweak penguin sector.

The connection between the Lorentz invariance violation in the Lagrangian context and the quantum theory of noncommutative fields is established for the $U(1)$ gauge field. The modified Maxwell equations coincide with other derivations obtained using different procedures. These modified equations are interpreted as describing macroscopic ones in a polarized and magnetized medium. A tiny magnetic field (seed) emerges as particular static solution that gradually increases once the modified Maxwell equations are solved as a self-consistent equations system.

Some quantum features of vortices in supersymmetric theories in $1+2$ dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one-loop while the spectrum of the elementary excitations receives higher-order corrections.

The breakdown of Lorentz and CPT invariance, as described by the extension of the standard model, gives rise to a modification of the dispersion relation of particles. Consequences of such a modification are reviewed in the framework of pulsar kicks induced by neutrino oscillations (active-sterile conversion). A peculiar feature of the modified energy-momentum relations is the occurrence of terms of the form $\delta \mathbf{\Pi }·\widehat{\mathbf{p}}$, where $\delta \mathbf{\Pi }$ accounts for the difference of spatial components of flavor depending coefficients which lead to the departure of the Lorentz symmetry, and $\widehat{\mathbf{p}}=\mathbf{p}/p$, being $\mathbf{p}$ the neutrino momentum. Owing to the relative orientation of $\mathbf{p}$ with respect to $\delta \mathbf{\Pi }$, the coupling $\delta \mathbf{\Pi }·\widehat{\mathbf{p}}$ may induce the mechanism to generate the observed pulsar velocities. Topics related to the velocity distribution of pulsars are also discussed.

We study issues of Lorentz violation symmetry in the context of the recently proposed theory of noncommutative fields [J. Carmona, J. L. Cortés, J. Gamboa, and F. Méndes, J. High Energy Phys. 03 (2003) 058; Phys. Lett. B 565, 222 (2003).], using the soldering formalism. To this end a noncommutative chiral boson with a deformed algebra [A. Das, J. Gamboa, F. Méndes, and J. Lópes-Sarrión, J. High Energy Phys. 05 (2004) 022.], used to study these notions in $D=2$, is properly generalized. We verify, also for this larger group of theories that, although the structure of the Lorentz group is preserved, the velocity of light is scaled by a function of the deformation parameter, as recently claimed. However, we found a subset of models where the velocity of propagation is maintained in spite of the presence of the deformed algebra. Effects of a preferred frame of reference manifest by the presence of birefringence were also studied in the chiral boson framework leading to the scalar sector of the extended standard model recently proposed.

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D nonlinear numerical evolutions of dynamical black-hole spacetimes.