In the context of threshold investigations of Lorentz violation, we discuss the fundamental principle of coordinate independence, the role of an effective dynamical framework, and the conditions of positivity and causality. Our analysis excludes a variety of previously considered Lorentz-breaking parameters and opens an avenue for viable dispersion-relation investigations of Lorentz violation.

The Weyl-gauge ${(A}_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss’s law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of S-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of “standard” perturbative states. The fact that the gauge-invariant chromoelectric field is not Hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this non-Hermiticity is taken into account, the “extra” vertices in the Christ-Lee’ Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this non-Hermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.

The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation and illustrated with detailed specific cases. Quantization is carried out with standard Hilbert space methods. With the proper physical interpretation, obtained by allowing for different time scales on different invariant sectors of a theory, the resulting non-Abelian approach to quantum Nambu mechanics is shown to be fully consistent.

Light Higgs bosons ${(h}^0)$ with a mass below 60 GeV may have escaped detection at CERN LEP due to a suppressed cross section for $e^{+}{e}^{-}\to {\mathrm{Zh}}^0.$ Their discovery is also problematic in standard search channels at the Fermilab Tevatron run II and LHC. Such an $h^0$ can arise in the two Higgs doublet model (2HDM) and in the minimal supersymmetric standard model (MSSM) with explicit CP violating phases. We propose the mechanism $p\overline{p}\to H^{\pm }{h}^0$ which offers cross sections of up to 500 fb in the 2HDM, or up to 100 fb in the MSSM. The possibility of a large branching ratio for $H^{\pm }\to h^0{W}^{\pm }$ would give rise to the nonstandard signature $h^0{h}^0{W}^{\pm }$ which might facilitate detection.

We study charmless two-body baryonic B decays in a diagrammatic approach. The relations for the decay amplitudes are obtained. In general there is more than one tree and more than one penguin amplitude. The number of independent amplitudes can be reduced in the large $m_B$ limit. This leads to more predictive results. Some prominent modes for experimental searches are pointed out.

Neutrinos at energies above TeV can serve as probes of the stellar progenitor and jet dynamics of gamma ray bursts arising from stellar core collapses. They can also probe collapses which do not lead to gamma rays, which may be much more numerous. We calculate detailed neutrino spectra from shock accelerated protons in jets just below the outer stellar envelope, before their emergence. We present neutrino flux estimates from such preburst jets for two different massive stellar progenitor models. These should be distinguishable by IceCube, and we discuss the implications.

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quarks and antiquarks in large $N_f$ QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, because of the fact that the two-loop running coupling of large $N_f$ QCD is explicitly written in terms of an analytic function, large $N_f$ QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large $N_f$ QCD.

In this note we show that in a two-dimensional noncommutative space the area operator is quantized; this outcome is compared with the result obtained by loop quantum gravity methods.

Focusing on the gauge degrees of freedom specified by a (1+3)-dimensional model accommodating a Maxwell term plus a Lorentz and $\mathrm{CPT}$ noninvariant Chern-Simons-like contribution, we obtain a minimal extension of such a system to a supersymmetric framework. We comment on the resulting peculiar self-couplings for the gauge sector, as well as on the background contribution for gaugino masses. Furthermore, a nonpolynomial generalization is presented.

We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates.

The Ward identities for amplitudes at the tree level are derived from the symmetries of the corresponding classical dynamical systems. The results are applied to some $\overrightarrow{2}n$ amplitudes.

We study the stability of five-dimensional Myers-Perry black holes with a single angular momentum under linear perturbations, and we compute the quasinormal modes of the black hole metric projected on the brane, using Leaver’s continued fraction method. In our numerical search we do not find unstable modes. The damping time of the modes having $l=m=2\mathrm{}$ and $l=m=1\mathrm{}$ tends to infinity as the black hole spin tends to the extremal value, showing a behavior reminiscent of the one observed for ordinary four-dimensional Kerr black holes.

The Penrose limits of inhomogeneous cosmologies admitting two Abelian Killing vectors and their Abelian T duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-Abelian T dualities are used as solution generating techniques. Furthermore, it is found that, unlike the case of Abelian T duality, non-Abelian T duality and taking the Penrose limit are not commutative procedures.

The simultaneous exchange of two pseudoscalars between fermions leads to a spin-independent force between macroscopic objects. Previous work has demonstrated that one can combine this interaction with tests of the weak equivalence principle, gravitational inverse square law, and studies of laser beam propagation in magnetic fields, to set significant new constraints on the Yukawa couplings of massless pseudoscalars to nucleons. Here we extend these results to massive pseudoscalars, and derive new constraints which relate the strengths of these couplings to the pseudoscalar mass.

We calculate the one-loop matching coefficients between continuum and lattice four-fermion operators for lattice operators constructed using staggered fermions and improved by the use of fattened links. In particular, we consider hypercubic fat links and $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$ projected fat-7 links, and their mean-field improved versions. We calculate only current-current diagrams, so that our results apply for operators whose flavor structure does not allow “eye diagrams.” We present general formulas, based on two independent approaches, and give numerical results for the cases in which the operators have the taste (staggered flavor) of the pseudo Goldstone pion. We find that the one-loop corrections are reduced down to the 10–20 % level, resolving the problem of large perturbative corrections for staggered fermion calculations of matrix elements.

We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges $g_V$ and $g_A.$ The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order ${O(a}^2).\mathrm{}$ The doubly blocked Wilson 2 (DBW2) gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and performing a high statistics simulation, we find a significant finite volume effect between the nucleon axial charges calculated on lattices with (1.2 ${\mathrm{f}\mathrm{m})}^3$ and (2.4 ${\mathrm{f}\mathrm{m})}^3$ volumes $\left(a\approx 0.15\mathrm{fm}\right).\mathrm{}$ On the large volume we find $g_A=1.212\mathrm{}\pm 0.027\left(\mathrm{stat}\right)\pm 0.024\left(\mathrm{norm}\right).\mathrm{}$ The quoted systematic error is the dominant (known) one, corresponding to current renormalization. We discuss other possible remaining sources of error. This theoretical first principles calculation, which does not yet include isospin breaking effects, yields a value of $g_A$ only a little bit below the experimental one, $1.2670\pm \mathrm{0.0030.}$

Results from several recent experiments provide indirect evidence in favor of the existence of a fourth generation neutrino. Such a neutrino with a mass m of about 50 GeV is compatible with current physical and astrophysical constraints and well motivated in the framework of superstring phenomenology. If sufficiently stable, the existence of such a neutrino leads to a drastic change in Higgs boson physics: for a wide range of Higgs boson masses the dominant mode of Higgs boson decay is invisible and the branching ratios for the most promising modes of Higgs boson search are significantly reduced. The proper strategy of Higgs boson searches in such a framework is discussed. It is shown that in the same framework the absence of a signal in the search for invisible Higgs boson decay at the CERN LEP means that the mass of the Higgs boson is greater than 113.5 GeV if the neutrino mass is about 50 GeV.

We construct a relativistic ${}^3{P}_0$ wave function for scalar mesons within the framework of the light-front quark model (LFQM). This scalar wave function is used to perform relativistic calculations of absolute widths for the radiative decay processes ${(0\mathrm{}}^{++})\to \gamma \gamma ,$ ${(0\mathrm{}}^{++})\to \phi \gamma ,$ and ${(0\mathrm{}}^{++})\to \rho \gamma$ which incorporate the effects of glueball-$q\overline{q}$ mixing. The mixed physical states are assumed to be $f_0\mathrm{}\left(1370\right),$ $f_0\mathrm{}\left(1500\right),$ and $f_0\mathrm{}\left(1710\right)\mathrm{}$ for which the flavor-glue content is taken from the mixing calculations of other works. Since experimental data for these processes are poor, our results are compared with those of a recent non-relativistic model calculation. We find that while the relativistic corrections introduced by the LFQM reduce the magnitudes of the decay widths by 50–70 %, the relative strengths between different decay processes are fairly well preserved. We also calculate decay widths for the processes $\overrightarrow{\phi }{(0\mathrm{}}^{++})\gamma$ and ${(0\mathrm{}}^{++})\to \gamma \gamma$ involving the light scalars $f_0\mathrm{}\left(980\right)\mathrm{}$ and $a_0\mathrm{}\left(980\right)\mathrm{}$ to test the simple $q\overline{q}$ model of these mesons. Our results of the $q\overline{q}$ model for these processes are not consistent with well-established data, further supporting the idea that $f_0\mathrm{}\left(980\right)\mathrm{}$ and $a_0\mathrm{}\left(980\right)\mathrm{}$ are not conventional $q\overline{q}$ states.

We study target mass effects in the polarized virtual photon structure functions $g_1^{\gamma }{(x,Q}^2{,P}^2),$ $g_2^{\gamma }{(x,Q}^2{,P}^2)$ in the kinematic region ${\Lambda }^2\ll P^2\ll Q^2,$ where $-Q^2\left(-P^2\right)$ is the mass squared of the probe (target) photon. We obtain the expressions for $g_1^{\gamma }{(x,Q}^2{,P}^2)$ and $g_2^{\gamma }{(x,Q}^2{,P}^2)$ in closed form by inverting the Nachtmann moments for the twist-2 and twist-3 operators. Numerical analysis shows that target mass effects appear at large x and become sizable near $x_{\max }[=1/[{1+(P}^2{/Q}^2\left)\right]],$ the maximal value of x, as the ratio $P^2{/Q}^2$ increases. Target mass effects for the sum rules of $g_1^{\gamma }$ and $g_2^{\gamma }$ are also discussed.