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I propose a self-dual deformation of the classical phase space of lattice Yang--Mills theory, in which both the electric and magnetic fluxes take value in the gauge Lie group.
Quantised Singularities in the Electromagnetic Field
Dirac, P. A. M, 1931 · 1931
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1977 Gauge theories and magnetic charge
Goddard, P, Nuyts, J, & Olive, D, · 1977
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1977 Magnetic monopoles as gauge particles?
Montonen, C & Olive, D, · 1977
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1979 Dyons of charge e θ \theta /2 π \pi
Witten, E, · 1979
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The Yang-Mills Equations Riemann Surfaces
Atiyah, M. F & Bott, R, 1983 · 1983
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The symplectic nature of fundamental groups of surfaces
Goldman, W. M, 1984 · 1984
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1986 New Variables for Classical and Quantum Gravity
Ashtekar, A, · 1986
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1988 Specialization of Ashtekar’s Formalism to Bianchi Cosmology
Kodama, H, · 1988
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1991 From “Quantum Groups” to “Quasi-Quantum Groups”
Kosmann-Schwarzbach, Y, · 1991
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1991 Invariants of 3-manifolds via link polynomials and quantum groups
Reshetikhin, N & Turaev, V. G, · 1991
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A categorical construction of 4D TQFTs
Crane, L & Yetter, D. N, 1993 · 1992
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1992 Two dimensional gauge theories revisited
Witten, E, · 1992
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Symplectic Forms on Moduli Spaces of Flat Connections on 2-manifolds
Jeffrey, L. C, 1994 · 1994
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1994 Symplectic structures associated to Lie-Poisson groups
Alekseev, A. Y & Malkin, A, · 1994
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1995 Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double
Frolov, S A, · 1995
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1995 Hamiltonian lattice gauge models and the Heisenberg double
Frolov, S A, · 1995
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1995 Real Ashtekar variables for Lorentzian signature space-times
Barbero G., J. F, · 1995
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1995 Symplectic Structure of the Moduli Space of Flat Connectionon a Riemann Surface
Alekseev, A. Y, & Malkin, A, · 1995
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1997 Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface
Frolov, S A, · 1997
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Lectures on the Geometry of Quantization
Bates, S & Weinstein, A, 1997 · 1997
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1997 Introduction to Electromagnetic Duality
Olive, D, · 1997
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1998 Lie group valued moment maps
Alekseev, A. Y, Malkin, A, & Meinrenken, E, · 1998
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Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix
Fock, V. V & Rosly, A. A, 1999 · 1999
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2000 Manin Pairs and Moment Maps
Alekseev, A & Kosmann-Schwarzbach, Y, · 2000
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Quasi-Poisson Manifolds
Alekseev, A. Y, Kosmann-Schwarzbach, Y, & Meinrenken, E, 2000 · 2000
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Haggard, H. M, Han, M, & Riello, A, · 2001
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2002 Duistermaat—Heckman measures and moduli spaces of flat bundles over surfaces
Alekseev, A. Y, Meinrenken, E, & Woodward, C. T, · 2002
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2002 Cosmological Deformation of Lorentzian Spin Foam Models
Noui, K & Roche, P, · 2002
2014 Observables in loop quantum gravity with a cosmological constant
Dupuis, M & Girelli, F, · 2014
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2014 Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
Dupuis, M, Girelli, F, & Livine, E. R, · 2014
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Deformed phase space for 3d loop gravity and hyperbolic discrete geometries
Bonzom, V, Dupuis, M, Girelli, F, & Livine, E. R, 2014 · 2014
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2014 Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
Bonzom, V, Dupuis, M, & Girelli, F, · 2014
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2014 A new vacuum for Loop Quantum Gravity
Dittrich, B & Geiller, M, · 2014
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SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry
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2003 Diffeomorphisms and spin foam models
Freidel, L & Louapre, D, · 2003
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2003 Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
Gukov, S, · 2003
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Convex Polyhedra
Alexandrov, A D, 2005 · 2005
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2006 Three-dimensional loop quantum gravity: Particles and the quantum double
Noui, K, · 2006
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2007 Observables in the Turaev-Viro and Crane-Yetter models
Barrett, J. W, Faria Martins, J, & Garcia-Islas, J. M, · 2007
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Quantum Gravity
Rovelli, C, 2007 · 2007
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Haggard, H. M, Han, M, Kamiński, W, & Riello, A, 2015 · 2015
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2015 Closure constraints for hyperbolic tetrahedra
Charles, C & Livine, E. R, · 2015
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2015 Twisted gauge theory model of topological phases in three dimensions
Wan, Y, Wang, J. C, & He, H, · 2015
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2015 Flux formulation of loop quantum gravity: classical framework
Dittrich, B & Geiller, M, · 2015
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A new realization of quantum geometry
Bahr, B, Dittrich, B, & Geiller, M, 2015 · 2015
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Haggard, H. M, Han, M, Kamiński, W, & Riello, A, · 2016
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From 3D TQFTs to 4D models with defects
Delcamp, C & Dittrich, B, 2016 · 2016
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Hopf algebra gauge theory on a ribbon graph
Meusburger, C & Wise, D. K, 2016 · 2016
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Dichromatic state sum models for four-manifolds from pivotal functors
Bärenz, M & Barrett, J. W, 2016 · 2016
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2016 The Fock space of loopy spin networks for quantum gravity
Charles, C & Livine, E. R, · 2016
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2017 SU(2) flat connection on a Riemann surface and 3D twisted geometry with a cosmological constant
Han, M & Huang, Z, · 2017
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Dittrich, B, · 2017
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2017 The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
Charles, C & Livine, E. R, · 2017
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2017 Kitaev Lattice Models as a Hopf Algebra Gauge Theory
Meusburger, C, · 2017
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Lan, T, Kong, L, & Wen, X.-G, 2017 · 2017
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2017 Quantum gravity kinematics from extended TQFTs
Dittrich, B & Geiller, M, · 2017
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2016 Fusion basis for lattice gauge theory and loop quantum gravity
Delcamp, C, Dittrich, B, & Riello, A, · 2017
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