Spin foam quantization and anomalies

Bojowald, Martin; Pérez, Alejandro

doi:10.1007/s10714-009-0892-9

Cited by 45 publications

(93 citation statements)

References 39 publications

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“…This in particular means that the boundary of each face contains each edge at most once. With certain choices for amplitudes, this condition can be relaxed slightly; see, for example, [85][86][87].…”

Section: Endnotesmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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Section: Endnotesmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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“…In [75] we gave a rigorous expression where the correct measure factor [22], resulting from the second class constraints involved in the Holst action, was included. This inclusion made sure that the path integral qualified as a reduced phase space quantisation of the theory, as it has been stressed in [95]. A similar analysis has been carried out for the Plebanski theory in [96], however, the resulting measure factor is widely ignored in the SFM literature.…”

Section: The Holst Spin Foam Model Via Cubulationsmentioning

confidence: 87%

Approaches to Quantum Gravity

Oriti

2009

215

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One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed.In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of 'space' and 'time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other.This thesis is divided in two parts: in the first part we analyse LQG, paying particular attention to the semiclassical properties of the volume operator. Such an operator plays a pivotal role in defining the dynamics of the theory, thus testing its semiclassical limit is of uttermost importance. We then proceed to analyse spin foam models (SFM), which are an attempt at a covariant or path integral formulation of canonical Loop Quantum Gravity (LQG). In particular, in this thesis we propose a new SFM, whose path integral is defined in terms of the Holst action rather than the Plebanski action (used in current SFM). This departure from current SFM has enabled us to solve, explicitly, certain constraints which seem rather problematic in the current SFM.In the second part of this thesis we introduce Topos theory and how it has been utilised to reformulate quantum theory in a way that a consistent quantum logic can be defined. Moreover, we also define a Topos formulation of history quantum theory. The striking difference of this approach and the current consistent-history approach is that, in the former no fundamental role is played by the notion of a consistent sets (set of histories which do not interfere with each other) while, in the latter, such notions are central. This is an exciting departure since one of the main difficulty in the consistenthistory approach is how to choose the correct consistent set of history propositions, since there are many sets, most of which incompatible. However, we have s...

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“…For theories with constraints and some interacting theories, this aim is non-trivial to obtain, and usually is not given by the heuristic Lebesgue measure. The obtention of the measure, has been a relevant step in developing of spin-foam models, which can be thought of as a path integral version of LQG [12,[35][36][37]. To cut a long story short (see e.g.…”

Section: {F{x)g{y)]d = {F{x)g{y)] -Jdudv{a{x)9'^{u)}d-'ß{mentioning

confidence: 99%

“…Nevertheless, the problem of the dynamics of the full theory has remained unsettled. In this respect, there are open issues as for instance how general relativity (GR) arises from LQG as a semiclassical limit of the quantum theory, and the fact that the algebra of quantum constraints, though free of anomalies, does not correspond to the algebra of classical constraints completely [12]. Purthermore, other problems are centered about the Hamiltonian constraint [13] which generates the dynamics of the system, unlike the gauge constraints associated with spatial diffeomorphisms and the internal gauge group remaining under control.…”

Section: Introductionmentioning

confidence: 99%

A Pure Dirac's Method for Husain–kuchar Theory

Escalante

Berra

2013

Int. J. Geom. Methods Mod. Phys.

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A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar (HK) model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and the gauge transformations for all variables that occur in the action principle. The complete set of constraints defined on the full phase space allow us to calculate the Dirac algebra structure of the theory and a local weighted measure for the path integral quantization method. Finally, we discuss briefly the necessary mathematical structure to perform the canonical quantization program within the framework of the loop quantum gravity approach.

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Spin foam quantization and anomalies

Cited by 45 publications

References 39 publications

Spin Foam Models with Finite Groups

Spin Foam Models with Finite Groups

Approaches to Quantum Gravity

A Pure Dirac's Method for Husain–kuchar Theory

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