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Coarse graining methods for spin net and spin foam models
 HOLONOMY SPIN FOAM MODELS: DEFINITION AND COARSE GRAINING,” PHYS. REV. D 87, 044048 (2013) [ARXIV:1208.3388 [GRQC
, 2011
"... We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on fini ..."
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Cited by 19 (11 self)
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We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce ‘cutoff models’ to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauß constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We
Smolin L., Disordered locality in loop quantum gravity states, Classical Quantum Gravity 24
"... We show that loop quantum gravity suffers from a potential problem with nonlocality, coming from a mismatch between microlocality, as defined by the combinatorial structures of their microscopic states, and macrolocality, defined by the metric which emerges from the low energy limit. As a result, ..."
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Cited by 12 (1 self)
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We show that loop quantum gravity suffers from a potential problem with nonlocality, coming from a mismatch between microlocality, as defined by the combinatorial structures of their microscopic states, and macrolocality, defined by the metric which emerges from the low energy limit. As a result, the low energy limit may suffer from a disordered locality characterized by identifications of far away points. We argue that if such defects in locality are rare enough they will be difficult to detect.
Twodimensional quantum YangMills theory with corners
, 2006
"... The solution of quantum YangMills theory on arbitrary compact twomanifolds is well known. We bring this solution into a TQFTlike form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in ..."
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Cited by 11 (7 self)
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The solution of quantum YangMills theory on arbitrary compact twomanifolds is well known. We bring this solution into a TQFTlike form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in higher dimensions. We motivate this axiomatic system from a formal SchrödingerFeynman quantization procedure. We also discuss the physical meaning of unitarity, the concept of vacuum, (partial) Wilson loops and nonorientable surfaces.
Loop quantization as a continuum limit
"... We present an implementation of Wilson’s renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop quantized theories is constructed as a continuum limit of dynamics of effective theories. After presenting the general formalism we show as first explicit example ..."
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Cited by 4 (4 self)
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We present an implementation of Wilson’s renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop quantized theories is constructed as a continuum limit of dynamics of effective theories. After presenting the general formalism we show as first explicit example the 2d Ising field theory. It is an interacting relativistic quantum field theory with local degrees of freedom quantized by loop quantization techniques. 1 Introduction and summary of results Loop Quantization was originally motivated by its application to theories free of a background metric like gravity and gravity coupled to matter. However, an extended version of the formalism sometimes referred to as a “polymer representation ” has been developed for gauge theories with compact
Renormalization of latticeregularized quantum gravity models I. General considerations
, 2014
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Free vacuum for loop quantum gravity
, 2005
"... We linearize extended ADMgravity around the flat torus, and use the associated Fock vacuum to construct a state that could play the role of a “free ” vacuum in loop quantum gravity. The state we obtain is an element of the gaugeinvariant kinematic Hilbert space and restricted to a cutoff graph, as ..."
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Cited by 1 (0 self)
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We linearize extended ADMgravity around the flat torus, and use the associated Fock vacuum to construct a state that could play the role of a “free ” vacuum in loop quantum gravity. The state we obtain is an element of the gaugeinvariant kinematic Hilbert space and restricted to a cutoff graph, as a natural consequence of the momentum cutoff of the original Fock state. It has the form of a Gaussian superposition of spin networks. We show that the peak of the Gaussian lies at weavelike states and derive a relation between the coloring of the weaves and the cutoff scale. Our analysis indicates that the peak weaves become independent of the cutoff length when the latter is much smaller than the Planck length. By the same method, we also construct multiplegraviton states. We discuss the possible use of these states for deriving a perturbation series in loop quantum gravity. 1