Towards new background independent representations for Loop Quantum Gravity

Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).Comment: 22 pages, minor change

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

Properties of the Volume Operator in Loop Quantum Gravity I: Results

We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in Loop Quantum Gravity, which is the quantum analogue of the classical volume expression for regions in three dimensional Riemannian space. Our analysis considers for the first time generic graph vertices of valence greater than four. Here we find that the geometry of the underlying vertex characterizes the spectral properties of the volume operator, in particular the presence of a `volume gap' (a smallest non-zero eigenvalue in the spectrum) is found to depend on the vertex embedding. We compute the set of all non-spatially diffeomorphic non-coplanar vertex embeddings for vertices of valence 5--7, and argue that these sets can be used to label spatial diffeomorphism invariant states. We observe how gauge invariance connects vertex geometry and representation properties of the underlying gauge group in a natural way. Analytical results on the spectrum on 4-valent vertices are included, for which the presence of a volume gap is proved. This paper presents our main results; details are provided by a companion paper arXiv:0706.0382v1.Comment: 36 pages, 7 figures, LaTeX. See also companion paper arXiv:0706.0382v1. Version as published in CQG in 2008. See arXiv:1003.2348 for important remarks regarding the sigma configurations. Subsequent computations have revealed some minor errors, which do not change the qualitative results but modify some of the numbers presented her

Loop Quantum Gravity a la Aharonov-Bohm

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.Comment: 19 pages, 1 figure; v2: corrected typos, section 4 expanded

On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.Comment: 43 page

Spherically Symmetric Quantum Geometry: Hamiltonian Constraint

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.Comment: 33 page

Discovery of very-high-energy emission from RGB J2243+203 and derivation of its redshift upper limit

Very-high-energy (VHE; $>$ 100 GeV) gamma-ray emission from the blazar RGB J2243+203 was discovered with the VERITAS Cherenkov telescope array, during the period between 21 and 24 December 2014. The VERITAS energy spectrum from this source can be fit by a power law with a photon index of $4.6 \pm 0.5$, and a flux normalization at 0.15 TeV of $(6.3 \pm 1.1) \times 10^{-10} ~ \textrm{cm}^{-2} \textrm{s}^{-1} \textrm{TeV}^{-1}$. The integrated \textit{Fermi}-LAT flux from 1 GeV to 100 GeV during the VERITAS detection is $(4.1 \pm 0.8) \times 10^{\textrm{-8}} ~\textrm{cm}^{\textrm{-2}}\textrm{s}^{\textrm{-1}}$, which is an order of magnitude larger than the four-year-averaged flux in the same energy range reported in the 3FGL catalog, ($4.0 \pm 0.1 \times 10^{\textrm{-9}} ~ \textrm{cm}^{\textrm{-2}}\textrm{s}^{\textrm{-1}}$). The detection with VERITAS triggered observations in the X-ray band with the \textit{Swift}-XRT. However, due to scheduling constraints \textit{Swift}-XRT observations were performed 67 hours after the VERITAS detection, not simultaneous with the VERITAS observations. The observed X-ray energy spectrum between 2 keV and 10 keV can be fitted with a power-law with a spectral index of $2.7 \pm 0.2$, and the integrated photon flux in the same energy band is $(3.6 \pm 0.6) \times 10^{-13} ~\textrm{cm}^{-2} \textrm{s}^{-1}$. EBL model-dependent upper limits of the blazar redshift have been derived. Depending on the EBL model used, the upper limit varies in the range from z $<~0.9$ to z $<~1.1$

Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in 3-dimensional Riemannian space, and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid. Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of [4-5], and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3, and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin \jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large \jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos corrected, presentation slightly extende

Investigating the TeV Morphology of MGRO J1908+06 with VERITAS

We report on deep observations of the extended TeV gamma-ray source MGRO J1908+06 made with the VERITAS very high energy (VHE) gamma-ray observatory. Previously, the TeV emission has been attributed to the pulsar wind nebula (PWN) of the Fermi-LAT pulsar PSR J1907+0602. We detect MGRO J1908+06 at a significance level of 14 standard deviations (14 sigma) and measure a photon index of 2.20 +/- 0.10_stat +/- 0.20_sys. The TeV emission is extended, covering the region near PSR J1907+0602 and also extending towards SNR G40.5--0.5. When fitted with a 2-dimensional Gaussian, the intrinsic extension has a standard deviation of sigma_src = 0.44 +/- 0.02 degrees. In contrast to other TeV PWNe of similar age in which the TeV spectrum softens with distance from the pulsar, the TeV spectrum measured near the pulsar location is consistent with that measured at a position near the rim of G40.5--0.5, 0.33 degrees away.Comment: To appear in ApJ, 8 page

Very-high-energy observations of the binaries V 404 Cyg and 4U 0115+634 during giant X-ray outbursts

Transient X-ray binaries produce major outbursts in which the X-ray flux can increase over the quiescent level by factors as large as $10^7$. The low-mass X-ray binary V 404 Cyg and the high-mass system 4U 0115+634 underwent such major outbursts in June and October 2015, respectively. We present here observations at energies above hundreds of GeV with the VERITAS observatory taken during some of the brightest X-ray activity ever observed from these systems. No gamma-ray emission has been detected by VERITAS in 2.5 hours of observations of the microquasar V 404 Cyg from 2015, June 20-21. The upper flux limits derived from these observations on the gamma-ray flux above 200 GeV of F $< 4.4\times 10^{-12}$ cm$^{-2}$ s$^{-1}$ correspond to a tiny fraction (about $10^{-6}$) of the Eddington luminosity of the system, in stark contrast to that seen in the X-ray band. No gamma rays have been detected during observations of 4U 0115+634 in the period of major X-ray activity in October 2015. The flux upper limit derived from our observations is F $< 2.1\times 10^{-12}$ cm$^{-2}$ s$^{-1}$ for gamma rays above 300 GeV, setting an upper limit on the ratio of gamma-ray to X-ray luminosity of less than 4%.Comment: Accepted for publication in the Astrophysical Journa