In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator and quantum dynamics are controlled by the difference equation. In this framework, Bojowald [M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).] showed that the initial singularity is absent in the twofold sense: (i) the spectrum of the inverse scale factor operator is bounded from above; (ii) the wave function of the Universe can be uniquely extended beyond the point which was the initial singularity in classical theory. In this paper, we study the initial singularity in this sense and the large-volume limit against the ambiguities in the discretization and the operator ordering within a homogeneous, isotropic and spatially flat model with the cosmological constant. We find that the absence of the singularity strongly depends on the choice of the operator ordering and the requirement for the absence singles out a very small class of orderings. Moreover we find a general ordering rule required for the absence of the singularity. We also find that the large-volume limit naturally recovers a smooth wave function in the discretization where each step corresponds to a fixed volume increment but not in the one where each step corresponds to a fixed area increment. If loop quantum cosmology is to be a phenomenological realization of full loop quantum gravity, these results are important to fix the theoretical ambiguities.

Dynamical Chern-Simons gravity is an interesting extension of general relativity, which finds its way in many different contexts, including string theory, cosmological settings, and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasicircular inspiralling of a small, stellar-mass object into a large nonrotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green’s function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively.

It has recently been pointed out that arbitrary center-of-mass energies may be obtained for particle collisions near the horizon of an extremal Kerr black hole. We investigate this mechanism in cylindrical topology. In particular we consider the center-of-mass energies of a cylindrical black hole with an extremal rotation and charge parameter. The geodesics are first derived with a rotating charged cylindrical black hole producing the background gravitational field. Finally the center-of-mass is determined for this background and its extremal limit is taken.

We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: $g^{\mu \nu }={\eta }^{\mu \nu }+{ϵ}^{\mu \nu }F(k·x)$, where ${ϵ}^{\mu \nu }$ is a constant polarization tensor, and $k_{\mu }$ is a lightlike vector. We also assume the coordinate gauge condition $|g{|}^{-1/4}{\partial }_{\tau }(|g{|}^{1/4}{g}^{\sigma \tau })=0$ which is the conformal analog of the harmonic gauge condition $g^{\mu \nu }{\Gamma }_{\mu \nu }^{\sigma }=-|g{|}^{-1/2}{\partial }_{\tau }(|g{|}^{1/2}{g}^{\sigma \tau })=0$, where $\det [g_{\mu \nu }]\equiv g$. Requiring additionally the conformal gauge condition $g=-1$ surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that ${ϵ}^{\mu \nu }$ be small. This implies that we have, in fact, exact plane-wave solutions; however, they are simply coordinate/conformal artifacts. As a consequence, they carry no energy. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form $g^{\mu \nu }={\eta }^{\mu \nu }+B^{\mu \nu }(n·x)G(k·x)$, indeed yields waves which carry energy and momentum [P. D. Mannheim, Gen. Relativ. Gravit. 43, 703 (2010)]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.

We study the effects of finite stellar temperatures on the oscillations of superfluid neutron stars. The importance of these effects is illustrated with a simple example of a radially pulsating general relativistic star. Two main effects are taken into account: (i) temperature dependence of the entrainment matrix and (ii) the variation of the size of superfluid region with temperature. Four models are considered, which include either one or both of these two effects. Pulsation spectra are calculated for these models, and asymptotes for eigenfrequencies at temperatures close to critical temperature of neutron superfluidity are derived. It is demonstrated that models that allow for the temperature effect (ii) but disregard the effect (i), yield unrealistic results. Eigenfunctions for the normal- and superfluid-type pulsations are analyzed. It is shown that superfluid pulsation modes practically do not appear at the neutron-star surface and, therefore, can hardly be observed by measuring the modulation of the electromagnetic radiation from the star. The e-folding times for damping of pulsations due to the shear viscosity and nonequilibrium modified Urca processes are calculated and their asymptotes at temperatures close to the neutron critical temperature, are obtained. It is demonstrated that superfluid pulsation modes are damped by 1–3 orders of magnitude faster than normal modes.

We study the effects of instrumental systematics on the estimation of primordial non-Gaussianity using the cosmic microwave background (CMB) bispectrum from both the temperature and the polarization anisotropies. For temperature systematics we consider gain fluctuation and beam distortions. For polarization we consider effects related to known instrumental systematics: calibration, pixel rotation, differential gain, pointing, and ellipticity of the instrument beam. We consider these effects at the next to leading order, which we refer to as nonlinear systematic effects. We find that if the instrumental response is linearly proportional to the received CMB intensity, then only the shape of the primordial CMB bispectrum, if there is any, will be distorted. We show that the nonlinear response of the instrument can in general result in spurious non-Gaussian features on both the CMB temperature and polarization anisotropies, even if the primordial CMB is completely Gaussian. We determine the level for both the linear and nonlinear systematics parameters for which they would cause no significant degradation of our ability to constrain the primordial non-Gaussianity amplitude $f_{\mathrm{NL}}$. We find that the nonlinear systematics are potentially a bigger worry for extracting the primordial non-Gaussianity than the linear systematics, especially because the current and near future CMB probes are optimized for CMB power-spectrum measurements which are not particularly sensitive to the nonlinear instrument response. We find that if instrumental nonlinearities are not controlled by dedicated calibration, the effective local non-Gaussianity can be as large as $f_{\mathrm{NL}}\sim O(10)$ before the corresponding nonlinearities show up in the CMB dipole measurements. The higher-order multipoles are even less sensitive to instrumental nonlinearities.

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge-invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge-invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion, i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on field theory.

We extend the standard model by adding two gauge-singlet ${\mathbb{Z}}_2$-symmetric scalar fields that interact with visible matter only through the Higgs particle. One is a stable dark matter WIMP, and the other one undergoes a spontaneous breaking of the symmetry that opens new channels for the dark matter annihilation, hence lowering the mass of the WIMP. We study the effects of the observed dark matter relic abundance on the WIMP annihilation cross section and find that in most regions of the parameters’ space, light dark matter is viable. We also compare the elastic-scattering cross section of our dark matter candidate off a nucleus with existing (CDMSII and XENON100) and projected (SuperCDMS and XENON1T) experimental exclusion bounds. We find that most of the allowed mass range for light dark matter will be probed by the projected sensitivity of the XENON1T experiment.

We study the electric conductivity induced by the magnetic field $B$ in quenched $SU(2)$ lattice gauge theory at a finite temperature below the deconfinement phase transition as a function of the bare quark mass $m_q$ in the range $m_q=55\mathrm{MeV}\dots 540\mathrm{MeV}$. At fixed quark mass, the conductivity grows linearly with the magnetic field strength $|B|$. The proportionality coefficient in this dependence increases towards smaller quark masses and seems to saturate at some finite value in the zero-mass limit. The nonanalytic dependence on the field strength might result from the mixing between vector mesons and pions in an external magnetic field. We discuss the implications of our results for dilepton angular distributions in heavy-ion collisions.

With accumulation of high statistics data at BESIII, one may study many new interesting channels. Among them, $J/\psi \to B^{*}\overline{B}+{\overline{B}}^{*}B\to \gamma B\overline{B}$ processes may provide valuable information of the radiative decays of the excited baryons $B^{*}(N^{*},{\Lambda }^{*},{\Sigma }^{*},{\Xi }^{*})$, and may shed light on their internal quark-gluon structure. Our estimation for the branching ratios of the nucleon excitations $N^{*}(1440)$, $N^{*}(1535)$ and $N^{*}(1520)$ from the reaction $J/\psi \to N^{*}\overline{p}+{\overline{N}}^{*}p\to p\overline{p}\gamma$, indicates that these processes can be studied at BESIII with ${10}^{10}J/\psi$ events. Explicit theoretical formulas for the partial wave analysis (PWA) of the $J/\psi \to B^{*}\overline{B}+{\overline{B}}^{*}B$ with $B^{*}\to B\gamma$ and ${\overline{B}}^{*}\to \overline{B}\gamma$ within covariant L-S Scheme are provided.

We employ the $B\to \pi$ form factors obtained from QCD light-cone sum rules and calculate the $B\to \pi \ell {\nu }_{\ell }$ width ($\ell =e$, $\mu$) in units of $1/|V_{ub}{|}^2$, integrated over the region of accessible momentum transfers, $0\le q^2\le 12.0{\mathrm{GeV}}^2$. Using the most recent BABAR Collaboration measurements we extract $|V_{ub}|=({3.50}_{-0.33}^{+0.38}{|}_{\mathrm{th}}\pm 0.11{|}_{\exp })\times {10}^{-3}$. The sum rule results for the form factors, taken as an input for a $z$-series parametrization, yield the $q^2$ shape in the whole semileptonic region of $B\to \pi \ell {\nu }_{\ell }$. We also present the charged lepton energy spectrum in this decay. Furthermore, the current situation with $B\to \tau {\nu }_{\tau }$ is discussed from the QCD point of view. We suggest using the ratio of the $B\to \pi \tau {\nu }_{\tau }$ and $B\to \pi \ell {\nu }_{\ell }(\ell =\mu ,e)$ widths as an additional test of the standard model. The sensitivity of this observable to new physics is illustrated by including a charged Higgs-boson contribution in the semileptonic decay amplitude.

We study the decay of dynamically generated resonances from the interaction of two vectors into a $\gamma$ and a pseudoscalar meson. The dynamics requires anomalous terms involving vertices with two vectors and a pseudoscalar, which renders it special. We compare our result with data on $K_2^{*+}(1430)\to K^{+}\gamma$ and $K_2^{*0}(1430)\to K^0\gamma$ and find a good agreement with the data for the $K_2^{*+}(1430)$ case and a width considerably smaller than the upper bound measured for the $K_2^{*0}(1430)$ meson. We also investigate the decay into ${\pi }^{+}\gamma$ of one $a_2$ state, tentatively associated to the $a_2(1320)$, obtaining qualitative agreement with data.

Active-sterile neutrino mixing is strongly constrained for $m_s\gtrsim 100\mathrm{keV}$ to avoid excessive energy losses from supernova cores. For smaller $m_s$, matter effects suppress the effective mixing angle except for a resonant range of energies where it is enhanced. We study the case of ${\nu }_{\tau }$-${\nu }_s$ mixing where a ${\nu }_{\tau }$-${\overline{\nu }}_{\tau }$ asymmetry builds up due to the strong excess of ${\nu }_s$ over ${\overline{\nu }}_s$ emission or vice versa, reducing the overall emission rate. In the warm dark matter range $m_s\lesssim 10\mathrm{keV}$ the mixing angle is essentially unconstrained.

We address the issue of evaluating chiral effects (such as the newly discovered chiral separation) in hydrodynamic approximation. The main tool we use is effective theory which defines interaction in terms of chemical potentials $\mu$, ${\mu }_5$. In the lowest order in $\mu$, ${\mu }_5$ we reproduce recent results based on thermodynamic considerations. In higher orders the results depend on details of infrared cutoff. Another point of our interest is an alternative way of the anomaly matching through introduction of effective scalar fields arising in the hydrodynamic approximation.

We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in $N=2$ projective superspace (“projective hyperspace”). With these, we are able to calculate both the divergent and finite parts of 2, 3, & 4-point functions at 1-loop for $N=2$ super-Yang-Mills theory), explicitly in projective hyperspace itself. We find that effectively only the coupling constant needs to be renormalized, unlike in the $N=1$ case where an independent wavefunction renormalization is also required. This feature is similar to that of the background field gauge, even though we are using ordinary Fermi-Feynman gauge. The computation of 1-hoop beta-function is then straightforward and matches with the known result. We also show that it receives no 2-hoops contributions. All these calculations provide an alternative proof of the finiteness of $N=4$ super-Yang-Mills.

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in the geometry of two parallel plates on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The nontrivial topology of the background spacetime leads to an Aharonov-Bohm effect for the vacuum expectation values induced by the gauge field. The fermionic condensate and the expectation value of the energy-momentum tensor are periodic functions of the magnetic flux with period equal to the flux quantum. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phases in the periodicity conditions and of the value of the gauge potential. Interaction forces between the plates are thus always attractive. However, in physical situations where the quantum field is confined to the region between the plates, the pure topological part contributes as well, and then the resulting force can be either attractive or repulsive, depending on the specific phases encoded in the periodicity conditions along the compact dimensions, and on the gauge potential, too. Applications of the general formulas to cylindrical carbon nanotubes are considered, within the framework of a Dirac-like theory for the electronic states in graphene. In the absence of a magnetic flux, the energy density for semiconducting nanotubes is always negative. For metallic nanotubes the energy density is positive for long tubes and negative for short ones. The resulting Casimir forces acting on the edges of the nanotube are attractive for short tubes with independence of the tube chirality. The sign of the force for long nanotubes can be controlled by tuning the magnetic flux. This opens the way to the design of efficient actuators driven by the Casimir force at the nanoscale.

We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number $N$ of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of $N$ modes with discrete energies $E_i$ with $i=1,\dots ,N$. We use this equivalence to derive the analytic solution for two-mode (bimodal) coherence, relevant for spectral-split formation in supernova neutrinos.

We discuss thermodynamics of electromagnetic radiation, with $p=(1/3)\rho$ and $S\propto T^{3}V$, and of cosmic string loops, with $p=-(1/3)\rho$ and $S\propto T^{-3}V$, where $p$ stands for pressure, $T$ temperature, $\rho$ energy density, $S$ entropy, and $V$ volume. We write the thermodynamic formalisms under a common framework that illustrates their formal relationship and allows us to go from one to the other through a smooth transformation. From a microscopic perspective, these relations arise from the energy relations $u(\lambda )=hc/\lambda$ for the photons of electromagnetic radiation, and $u(l)=(c^4/a^{2}G)l$ for cosmic string loops, $a$ being a numerical (dimensionless) constant and $\lambda$ and $l$ the radiation wavelength and the length of a loop; $G$, $c$, and $h$ are the gravitational constant, the speed of light in vacuo, and the Planck constant, respectively. The corresponding thermodynamic behaviors are seen to be connected through a related thermal duality corresponding to the change of $T$ by $T^{*}=T_c^2/T$, with $T_c$ a reference temperature related to $h$, $c$, and $G$.

We study the dynamics of strings by means of a distribution function $f(\mathbf{A},\mathbf{B},\mathbf{x},t)$, defined on a $9+1\mathrm{D}$ phase space, where $\mathbf{A}$ and $\mathbf{B}$ are the correlation vectors of right- and left-moving waves. We derive a transport equation (analogous to a Boltzmann transport equation for particles) that governs the evolution of long strings with Nambu-Goto dynamics, as well as reconnections taken into account. We also derive a system of coupled transport equations (analogous to a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for particles) which can simultaneously describe long strings $\tilde{f}(\mathbf{A},\mathbf{B},\mathbf{x},t)$ as well as simple loops $\stackrel{\circ }{f}(\mathbf{A},\mathbf{B},\mathbf{x},t)$ made out of four correlation vectors. The formalism can be used to study nonlinear dynamics of fundamental strings, $D$-brane strings, or field theory strings. For example, the complicated semiscaling behavior of cosmic strings translates into a simple solution of the transport system at small energy densities.

We propose central exclusive production of a charged Higgs boson in association with a $W$ boson as a possible signature of certain types of extended Higgs sectors. We calculate the cross section and find that the rate at the LHC could be large enough to allow observation in some models with two-Higgs doublets, where the charged Higgs and at least one of the neutral scalars can be light enough. We use the two-Higgs doublet model as a prototype and consider two distinct regions of parameter space, but we also briefly discuss the prospects for the next-to-minimal supersymmetric standard model, where the charged Higgs may very well be quite light.