From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

CODE ultra-rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context an ultra-rapid solution series is generated considering GPS and GLONASS satellites. It is updated several times per day and contains 24 hours of observed and 24 hours of predicted orbit interval. More details are available in: Lutz, S., G. Beutler, S. Schaer, R. Dach, A. Jäggi; 2014: CODE's new ultra-rapid orbit and ERP products for the IGS. GPS Solutions. DOI 10.1007/s10291-014-0432-2

CODE repro2 product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: • Astronomical Institute, University of Bern (AIUB), Bern, Switzerland • Federal Office of Topography swisstopo, Wabern, Switzerland • Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany • Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany It acts as a global analysis center of the International GNSS Service (IGS, Dow et al, 2009). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context the contribution to the IGS repro02 effort is generated considering only the GPS satellites between 1994 and 2001 as well as the GPS and GLONASS satellites from 2002 to the end of 2013.

CODE rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland;Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context a rapid solution series is generated considering all active GPS and GLONASS satellites. It contains 24 hours of observed orbits and published at the day after the observations.

CODE final product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions:Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a final solution series is generated considering all active GPS and GLONASS satellites. It is published in daily files with a delay of about two weeks.

CODE product series for the IGS-MGEX project

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a multi-GNSS solution is generated considering all active GPS, GLONASS, Galileo, BeiDou (expect for GEOs), and QZSS satellites as a contribution to the IGS-MGEX project. The results are published with a delay of about two weeks.

The CODE MGEX orbit and clock solution

The Center for Orbit Determination in Europe (CODE) is contributing as a global Analysis center to the International GNSS Service (IGS) since many years. The processing of GPS and GLONASS data is well established in CODE’s ultra-rapid, rapid, and final product lines. With the introduction of new signals for the established and new GNSS, new challenges and opportunities are arising for the GNSS data management and processing. The IGS started the Multi-GNSS-EXperiment (MGEX) in 2012 in order to gain first experience with the new data formats and to develop new strategies for making optimal use of these additional measurements. CODE has started to contribute to IGS MGEX with a consistent, rigorously combined triple-system orbit solution (GPS, GLONASS, and Galileo). SLR residuals for the computed Galileo satellite orbits are of the order of 10 cm. Furthermore CODE established a GPS and Galileo clock solution. A quality assessment shows that these experimental orbit and clock products allow even a Galileo-only precise point positioning (PPP) with accuracies on the decimeter- (static PPP) to meter-level (kinematic PPP) for selected stations.