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To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex.
Representation theory of analytic holonomy c*-algebras
A. Ashtekar and J. Lewandowski · 1994
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Topological measure and graph-differential geometry on the quotient space of connections
J. Lewandowski · 1994
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Differential geometry on the space of connections via graphs and projective limits
A. Ashtekar and J. Lewandowski · 1995
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Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, and T. Thiemann · 1995
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Discreteness of area and volume in quantum gravity
C. Rovelli and L. Smolin · 1995
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Barbero’s hamiltonian derived from a generalized hilbert-palatini action
S. Holst · 1996
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Q ^ \mathrm{Q\hat{}{}} operator for canonical quantum gravity
Y. Ma and Y. Ling · 2000
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An introduction to spin foam models of bf theory and quantum gravity
J. C. Baez · 2000
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Absence of a singularity in loop quantum cosmology
M. Bojowald · 2001
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Spin foam models for quantum gravity
A. Perez · 2003
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Mathematical structure of loop quantum cosmology
A. Ashtekar, M. Bojowald, J. Lewandowski, et al · 2003
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Methods of modern mathematical physics I: Functional analysis , volume 1
M. Reed and B. Simon · 2003
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Background independent quantum gravity: a status report
A. Ashtekar and J. Lewandowski · 2004
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quantum gravity
C. Rovelli · 2005
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Irreducibility of the ashtekar–isham–lewandowski representation
H. Sahlmann and T. Thiemann · 2006
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Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
J. Lewandowski, A. Okolow, H. Sahlmann, and T. Thiemann · 2006
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The phoenix project: master constraint programme for loop quantum gravity
T. Thiemann · 2006
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Master constraint operators in loop quantum gravity
M. Han and Y. Ma · 2006
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Quantum nature of the big bang: Improved dynamics
A. Ashtekar, T. Pawlowski, and P. Singh · 2006
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Fundamental structure of loop quantum gravity
M. Han, Y. Ma, and W. Huang · 2007
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Modern canonical quantum general relativity
T. Thiemann · 2007
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Cosmic recall and the scattering picture of loop quantum cosmology
W. Kamiński and T. Pawłowski · 2010
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The dynamics of the massless scalar field coupled to lqg in the polymer quantization
J. Lewandowski, M. Domagala, and M. Dziendzikowski · 2011
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New scalar constraint operator for loop quantum gravity
M. Assanioussi, J. Lewandowski, and I. Mäkinen · 2015
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Hamiltonian operator for loop quantum gravity coupled to a scalar field
E. Alesci, M. Assanioussi, J. Lewandowski, and I. Mäkinen · 2015
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Loop quantum cosmology from quantum reduced loop gravity
E. Alesci and F. Cianfrani · 2015
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New hamiltonian constraint operator for loop quantum gravity
J. Yang and Y. Ma · 2015
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K. Giesel and T. Thiemann · 2007
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Effective scenario of loop quantum cosmology
Y. Ding, Y. Ma, and J. Yang · 2009
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Alternative quantization of the hamiltonian in loop quantum cosmology
J. Yang, Y. Ding, and Y. Ma · 2009
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New length operator for loop quantum gravity
Y. Ma, C. Soo, and J. Yang · 2010
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Algebraic quantum gravity (aqg): Iv. reduced phase space quantization of loop quantum gravity
K. Giesel and T. Thiemann · 2010
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Gravity quantized: Loop quantum gravity with a scalar field
M. Domagała, K. Giesel, W. Kamiński, and J. Lewandowski · 2010
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New volume and inverse volume operators for loop quantum gravity
J. Yang and Y. Ma · 2016
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An embedding of loop quantum cosmology in variables into a full theory context
N. Bodendorfer · 2016
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Quantum cosmology from group field theory condensates: a review
S. Gielen and L. Sindoni · 2016
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Einstein equation from covariant loop quantum gravity in semiclassical continuum limit
M. Han · 2017
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Time evolution in deparametrized models of loop quantum gravity
M. Assanioussi, J. Lewandowski, and I. Mäkinen · 2017
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Graphical calculus of volume, inverse volume and hamiltonian operators in loop quantum gravity
J. Yang and Y. Ma · 2017
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Towards the self-adjointness of a hamiltonian operator in loop quantum gravity
C. Zhang, J. Lewandowski, and Y. Ma · 2018
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Cosmological effective hamiltonian from full loop quantum gravity dynamics
A. Dapor and K. Liegener · 2018
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