Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories

A unitary transformation \Ps [E]=\exp (i\O [E]/g) F[E] is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because \o^a_i\equiv -\d\O [E]/\d E^{ai} transforms as a (composite) connection. The geometric information in \o^a_i is transferred to a gauge invariant spatial connection \G^i_{jk} and torsion by a suitable choice of basis vectors for the adjoint representation which are constructed from the electric field $E^{ai}$. A metric is also constructed from $E^{ai}$. For gauge group $SU(2)$, the spatial geometry is the standard Riemannian geometry of a 3-manifold, and for $SU(3)$ it is a metric preserving geometry with both conventional and unconventional torsion. The transformed Hamiltonian is local. For a broad class of physical states, it can be expressed entirely in terms of spatial geometric, gauge invariant variables.Comment: 16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one reference added

The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds

In this fourth paper of the series, I clarify the somewhat mysterious relation between the large class of {\it orientation orbifolds} (with twisted open-string CFT's at $\hat c=52$) and {\it orientifolds} (with untwisted open strings at $c=26$), both of which have been associated to division by world-sheet orientation-reversing automorphisms. In particular -- following a spectral clue in the previous paper -- I show that, even as an {\it interacting string system}, a certain half-integer-moded orientation orbifold-string system is in fact equivalent to the archetypal orientifold. The subtitle of this paper, that orientation orbifolds include and generalize standard orientifolds, then follows because there are many other orientation orbifold-string systems -- with higher fractional modeing -- which are not equivalent to untwisted string systems.Comment: 22 pages, typos correcte

Bose-Einstein condensation in the presence of a uniform field and a point-like impurity

The behavior of an ideal $D$-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrarily to an old standing folklore, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\neq 0$ for $D=1,2,3$ if there is a point-like impurity at the bottom of the vessel containing the gas.Comment: 14 pages, REVTEX. Revised version, accepted for publication in Phys. Rev.

Perturbative Computation of the Gluonic Effective Action via Polyaokov's World-Line Path Integral

The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one (gluonic) loop effective action to fourth order in perturbation theory. The merits of the proposed approach is that, to a given order, it reduces to performing two integrations, one over a set of Grassmann and one over a set of Feynman-type parameters through which one manages to accomodate all Feynman diagrams entering the computation at once.Comment: 21 page

Epistasis not needed to explain low dN/dS

An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a phenomenon known as epistasis. In a recent letter to Nature, Breen et al. (2012) argued that epistasis must be "pervasive throughout protein evolution" because the observed ratio between the per-site rates of non-synonymous and synonymous substitutions (dN/dS) is much lower than would be expected in the absence of epistasis. However, when calculating the expected dN/dS ratio in the absence of epistasis, Breen et al. assumed that all amino acids observed in a protein alignment at any particular position have equal fitness. Here, we relax this unrealistic assumption and show that any dN/dS value can in principle be achieved at a site, without epistasis. Furthermore, for all nuclear and chloroplast genes in the Breen et al. dataset, we show that the observed dN/dS values and the observed patterns of amino acid diversity at each site are jointly consistent with a non-epistatic model of protein evolution.Comment: This manuscript is in response to "Epistasis as the primary factor in molecular evolution" by Breen et al. Nature 490, 535-538 (2012

CCO Pulsars as Anti-Magnetars: Evidence of Neutron Stars Weakly Magnetized at Birth

Our new study of the two central compact object pulsars, PSR J1210-5226 (P = 424 ms) and PSR J1852+0040 (P = 105 ms), leads us to conclude that a weak natal magnetic field shaped their unique observational properties. In the dipole spin-down formalism, the 2-sigma upper limits on their period derivatives, < 2E-16 for both pulsars, implies surface magnetic field strengths of B_s < 3E11 G and spin periods at birth equal to their present periods to three significant digits. Their X-ray luminosities exceed their respective spin-down luminosities, implying that their thermal spectra are derived from residual cooling and perhaps partly from accretion of supernova debris. For sufficiently weak magnetic fields an accretion disk can penetrate the light cylinder and interact with the magnetosphere while resulting torques on the neutron star remain within the observed limits. We propose the following as the origin of radio-quiet CCOs: the magnetic field, derived from a turbulent dynamo, is weaker if the NS is formed spinning slowly, which enables it to accrete SN debris. Accretion excludes neutron stars born with both B_s 0.1 s from radio pulsar surveys, where such weak fields are not encountered except among very old (> 40 Myr) or recycled pulsars. We predict that these birth properties are common, and may be attributes of the youngest detected neutron star, the CCO in Cassiopeia A, as well as an undetected infant neutron star in the SN 1987A remnant. In view of the far-infrared light echo discovered around Cas A and attributed to an SGR-like outburst, it is especially important to determine via timing whether Cas A hosts a magnetar or not. If not a magnetar, the Cas A NS may instead have undergone a one-time phase transition (corequake) that powered the light echo.Comment: 5 pages, 4 figures, Latex, aipproc.cls. To appear in the conference proceedings "40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More", held on August 12-17, 2007, at McGill University, Montreal, Canada; for further details see arXiv:0705.0978 and arXiv:0704.225