We analyze the structure of the Faddeev-Jackiw method and show that the canonical 2-form of the Lagrangian constructed in the last step of the Faddeev-Jackiw method is always nondegenerate. So according to the Darboux theorem, there must exist a coordinate transformation that can transform the Lagrangian into a standard form. We take the coordinates after the transformation as these in a phase space, and use this standard form of the Lagrangian, we achieve its path integral expression over the symplectic space, give the Faddeev-Jackiw canonical quantization of the path integral, and then we further show up the concrete application of the Faddeev-Jackiw canonical quantization of the path integral.

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary spacetimes. These expressions involve nonlocally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.

We study the reaction mechanism for the photoproduction of the $\Lambda (1520)$, based on an effective Lagrangian approach. We investigate each contribution of the $s$-, $u$-, $t$-channel processes and contact term, separately. One of the most characteristic features of this reaction is the contact-term dominance which governs the photoproduction from the proton, when the $K^{*}$-exchange contribution is possibly not too large. We suggest several different ways of the polarizations and arrangement of the beam and target to understand the role of each contribution separately in future experiments.

We consider a $\mu -\tau$ symmetry in neutrino sectors realized at the GUT scale in the context of a seesaw model. In our scenario, the exact $\mu -\tau$ symmetry realized in the basis where the charged lepton and heavy Majorana neutrino mass matrices are diagonal leads to vanishing lepton asymmetries. We find that, in the minimal supersymmetric extension of the seesaw model with large $\tan \beta$, the renormalization group (RG) evolution from the GUT scale to seesaw scale can induce a successful leptogenesis even without introducing any symmetry breaking terms by hand, whereas such RG effects lead to tiny deviations of ${\theta }_{23}$ and ${\theta }_{13}$ from $\pi /4$ and zero, respectively. It is shown that the right amount of the baryon asymmetry ${\eta }_B$ can be achieved via so-called resonant leptogenesis, which can be realized at rather low seesaw scale with large $\tan \beta$ in our scenario so that the well-known gravitino problem is safely avoided.

Braneworld models with induced gravity have the potential to replace dark energy as the explanation for the current accelerating expansion of the Universe. The original model of Dvali, Gabadadze, and Porrati (DGP) demonstrated the existence of a “self-accelerating” branch of background solutions, but suffered from the presence of ghosts. We present a new large class of braneworld models which generalize the DGP model. Our models have negative curvature in the bulk, allow a second brane, and have general brane tensions and localized curvature terms. We exhibit three different kinds of ghosts, associated to the graviton zero mode, the radion, and the longitudinal components of massive graviton modes. The latter two species occur in the DGP model, for negative and positive brane tension, respectively. In our models, we find that the two kinds of DGP ghosts are tightly correlated with each other, but are not always linked to the feature of self-acceleration. Our models are a promising laboratory for understanding the origins and physical meaning of braneworld ghosts, and perhaps for eliminating them altogether.

The realization that string theory gives rise to a huge landscape of vacuum solutions has recently prompted a statistical approach towards extracting phenomenological predictions from string theory. Unfortunately, for most classes of string models, direct enumeration of all solutions is not computationally feasible and thus statistical studies must resort to other methods in order to extract meaningful information. In this paper, we discuss some of the issues that arise when attempting to extract statistical correlations from a large data set to which our computational access is necessarily limited. Our main focus is the problem of “floating correlations.” As we discuss, this problem is endemic to investigations of this type and reflects the fact that not all physically distinct string models are equally likely to be sampled in any random search through the landscape, thereby causing statistical correlations to float as a function of sample size. We propose several possible methods that can be used to overcome this problem, and we show through explicit examples that these methods lead to correlations and statistical distributions which are not only stable as a function of sample size, but which differ significantly from those which would have been naïvely apparent from only a partial data set.

The spectrum of meson and diquark excitations in cold color superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with $\beta$ equilibrium. A two-flavored Nambu-Jona-Lasinio–type model including baryon ${\mu }_B$, color ${\mu }_8$, and electric ${\mu }_Q$ chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the $\beta$ equilibrium. The sensitivity of the model to the tuning of the interaction constants in the diquark ($H$) and quark-antiquark ($G$) channels is examined for two different parametrization schemes by choosing the ratio $H/G$ to be $3/4$ and 1, respectively. The gapless neutral color superconductivity is realized at $H=3G/4$, and the gapped neutral color superconductivity at $H=G$. It is shown that color and electrical neutrality together with $\beta$ equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non-neutral matter. The $\pi$- and $\sigma$-meson masses are evaluated to be $\sim 300\mathrm{MeV}$. It is also shown that the properties of the physical $SU(2{)}_c$-singlet diquark excitation in the 2SC ground state vary for different parametrization schemes. Thus, for $H=3G/4$ one finds a heavy resonance with mass $\sim 1100\mathrm{MeV}$ in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass $\sim |{\mu }_Q|\sim 200\mathrm{MeV}$ appears in the gapless 2SC environment. For a stronger attraction in the diquark channel ($H=G$), there is again a resonance (with the mass $\sim 300\mathrm{MeV}$) in the neutral gapped 2SC phase. Hence, the existence of the stable massive $SU(2{)}_c$-singlet diquark excitation is a new peculiarity of the gapless 2SC. In addition, the behavior of the diquark mass in vacuum, i.e., at ${\mu }_B=0$, as a function of $H$ has been investigated.

We calculate the nonzero Boer-Mulders functions of sea quarks inside the proton in a meson-baryon fluctuation model. The results show that the transverse spin effects of sea quarks in an unpolarized nucleon are sizable. Using the obtained antiquark Boer-Mulders functions, we estimate the $\cos 2\varphi$ asymmetries in the unpolarized $pp$ and $pD$ Drell-Yan processes at FNAL E866/NuSea experiments. The prediction for the $\cos 2\varphi$ asymmetries in the unpolarized $pp$ Drell-Yan process at the BNL Relativistic Heavy Ion Collider (RHIC) is also given.

We investigate the extent to which leptonic $CP$-violation in ($3+2$) sterile neutrino models leads to different oscillation probabilities for ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ and ${\nu }_{\mu }\to {\nu }_e$ oscillations at MiniBooNE. We are using a combined analysis of short-baseline (SBL) oscillation results, including the LSND and null SBL results, to which we impose additional constraints from atmospheric oscillation data. We obtain the favored regions in MiniBooNE oscillation probability space for both ($3+2$) $CP$-conserving and ($3+2$) $CP$-violating models. We further investigate the allowed $CP$-violation phase values and the MiniBooNE reach for such a $CP$ violation measurement. The analysis shows that the oscillation probabilities in MiniBooNE neutrino and antineutrino running modes can differ significantly, with the latter possibly being as much as 3 times larger than the first. In addition, we also show that all possible values of the single $CP$-violation phase measurable at short baselines in ($3+2$) models are allowed within 99% CL by existing data.

We present a new measurement of the $B^{+}$ meson differential cross section $d\sigma /d{p}_T$ at $\sqrt{s}=1960\mathrm{GeV}$. The data correspond to an integrated luminosity of $739{\mathrm{pb}}^{-1}$ collected with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider. $B^{+}$ candidates are reconstructed through the decay $B^{+}\to J/\psi K^{+}$, with $J/\psi \to {\mu }^{+}{\mu }^{-}$. The integrated cross section for producing $B^{+}$ mesons with $p_T\ge 6\mathrm{GeV}/c$ and $|y|\le 1$ is measured to be $2.78\pm 0.24\mu \mathrm{b}$.

We consider an extended supersymmetric SO(10) seesaw model with only doublet Higgs scalars, in which neutrino masses are suppressed by the scale of $D$-parity violation. Leptogenesis can occur at the TeV scale through the decay of a singlet $\Sigma$, thereby avoiding the gravitino crisis. Washout of the asymmetry can be effectively suppressed by the absence of direct couplings of $\Sigma$ to leptons.

In the Schrödinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta \equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the $Q$ operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source $j(t)$. These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitian transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.

We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.

We consider the recent calculation by Rovelli of the graviton propagator in the spinfoam formalism. Within the 3D toy model introduced by Speziale, we test how the spinfoam formalism can be used to construct the perturbative expansion of graviton amplitudes. Although the 3D graviton is a pure gauge, one can choose to work in a gauge where it is not zero and thus reproduce the structure of the 4D perturbative calculations. We compute explicitly the next-to-leading and next-to-next-to-leading orders, corresponding to one-loop and two-loop corrections. We show that while the first arises entirely from the expansion of the Regge action around the flat background, the latter receives contributions from the microscopic, non-Regge-like, quantum geometry. Surprisingly, this new contribution reduces the magnitude of the next-to-next-to-leading order. It thus appears that the spinfoam formalism is likely to substantially modify the conventional perturbative expansion at higher orders. This result supports the interest in this approach. We then address a number of open issues in the rest of the paper. First, we discuss the boundary state ansatz, which is a key ingredient in the whole construction. We propose a way to enhance the ansatz in order to make the edge lengths and dihedral angles conjugate variables in a mathematically well-defined way. Second, we show that the leading order is stable against different choices of the face weights of the spinfoam model; the next-to-leading order, on the other hand, is changed in a simple way, and we show that the topological face weight minimizes it. Finally, we extend the leading-order result to the case of a regular, but not equilateral, tetrahedron.

I examine thermodynamic fluctuations for a Kerr-Newman black hole in an extensive, infinite environment. This problem is not strictly solvable because full equilibrium with such an environment cannot be achieved by any black hole with mass $M$, angular momentum $J$, and charge $Q$. However, if we consider one (or two) of $M$, $J$, or $Q$ to vary so slowly compared with the others that we can regard it as fixed, instances of stability occur, and thermodynamic fluctuation theory could plausibly apply. I examine seven cases with one, two, or three independent fluctuating variables. No knowledge about the thermodynamic behavior of the environment is needed. The thermodynamics of the black hole is sufficient. Let the fluctuation moment for a thermodynamic quantity $X$ be $\sqrt{⟨(\Delta X{)}^2⟩}$. Fluctuations at fixed $M$ are stable for all thermodynamic states, including that of a nonrotating and uncharged environment, corresponding to average values $J=Q=0$. Here, the fluctuation moments for $J$ and $Q$ take on maximum values. That for $J$ is proportional to $M$. For the Planck mass it is $0.3990\hslash$. That for $Q$ is $3.301e$, independent of $M$. In all cases, fluctuation moments for $M$, $J$, and $Q$ go to zero at the limit of the physical regime, where the temperature goes to zero. With $M$ fluctuating there are no stable cases for average $J=Q=0$. But, there are transitions to stability marked by infinite fluctuations. For purely $M$ fluctuations, this coincides with a curve which Davies identified as a phase transition.

We present a Dirac quantization of generic single-horizon black holes in two-dimensional dilaton gravity. The classical theory is first partially reduced by a spatial gauge choice under which the spatial surfaces extend from a black or white hole singularity to a spacelike infinity. The theory is then quantized in a metric representation, solving the quantum Hamiltonian constraint in terms of (generalized) eigenstates of the ADM mass operator and specifying the physical inner product by self-adjointness of a time operator that is affinely conjugate to the ADM mass. Regularity of the time operator across the horizon requires the operator to contain a quantum correction that distinguishes the future and past horizons and gives rise to a quantum correction in the hole’s surface gravity. We expect a similar quantum correction to be present in systems whose dynamics admits black hole formation by gravitational collapse.

The closed, $k=1$, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the $k=0$ case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the “difficulties” pointed out by Green and Unruh in the $k=1$ case do not arise in a more systematic treatment. As in $k=0$ models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the $k=0$ case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna’s recent work addressed to computational physicists.

We consider a model in which massive stars form in a self-gravitating accretion disk around an active galactic nucleus (AGN). These stars may evolve and collapse to form compact objects on a time scale shorter than the accretion time, thus producing an important family of sources for LISA. Assuming the compact object formation/inspiral rate is proportional to the steady-state gas accretion rate, we use the intrinsic hard x ray AGN luminosity function to estimate expected event rates and signal strengths. We find that these sources will produce a continuous low-frequency $(\lesssim 1\mathrm{mHz})$ background detectable by LISA if more than $\sim 1\%$ of the accreted matter is in the form of compact objects. For compact objects with masses $\gtrsim 10M_{\odot }$, the last stages of the inspiral events should be resolvable above a few mHz, with rates as high as a few hundred per year.

We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic timelike geodesics have dependence on initial conditions. In contrast, the predictions extracted from “eternal” geodesics, which never enter terminal vacua, do not suffer from this problem. We derive measure equations for ensembles of geodesics and discuss possible interpretations of initial conditions in eternal inflation.

The loop quantization of the negatively curved $k=-1$ Robertson-Walker model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the $k=0$, $+1$ models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the $k=0$, $+1$ models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the $k=0$ model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.