Loop quantum cosmology and spin foams

Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam

doi:10.1016/j.physletb.2009.10.042

Cited by 76 publications

(154 citation statements)

References 16 publications

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“…Such resummation is just the analogue of the vertex expansion of the spin foam models that was identified in [31,32]. In contrast to the latter, however, for our mechanical models we have been able to compute the sums explicitly and hence derive an analytic propagator for each case.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, a detailed connection between the Hamiltonain LQG and the spin foam model for the case of homogeneous isotropic cosmic models has been developed [31,32] showing that both Hamiltonian transition amplitudes, time deparametrized and time reparametrization invariant, can be written in a vertex expansion form, typical of the spin foam models, and they actually coincide. Based on this, it is interesting to apply this method also to mechanical systems with finite degrees of freedom (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Sec. IV is devoted to present the method introduced in [31,32] to cast loop quantum cosmology in spin foam framework. Here we develop it for a single particle to be used in the following sections.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Path integral polymer propagator of relativistic and nonrelativistic particles

Morales‐Técotl¹,

Rastgoo²,

Ruelas³

2017

Phys. Rev. D

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A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method and as a new result we obtain the polymer propagator of the relativistic particle. All of them reduce to their standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Our results are robust thanks to their analytic and exact character which in turn come from the fact that presented models are solvable. They lend support to the vertex expansion scheme of the polymer path integral explored before in a formal way for cosmological models. Some possible future developments are commented upon in the discussion.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Path integral polymer propagator of relativistic and nonrelativistic particles

Morales‐Técotl¹,

Rastgoo²,

Ruelas³

2017

Phys. Rev. D

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“…The effective description of LQC is a delicate and topical issue since it may relate the quantum gravity effects to low-energy physics. The effective equations of LQC are being studied from both the canonical perspective [43][44][45][46] and the path integral perspective [47][48][49][50][51][52][53]. Since the key element in the polymer-like quantization of the previous subsection is to take holonomies rather than connections as basic variables, a heuristic and simple way to get the effective equations is to do the replacementc → sin(μc) µ [30].…”

Section: Effective Equationmentioning

confidence: 99%

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Zhang

2016

Universe

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Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans-Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed.

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“…Further, sLQC has also provided insights on the behavior of fluctuations across the bounce, which turn out to be tightly constrained, thus preserving semi-classicality, and showing that a semi-classical state before the bounce evolves to a semi-classical state after the bounce and vice versa [14,15,16]. sLQC has also led to insights on spin foam models using path integral approach [17,18,19] and on applications of consistent histories approach to quantization of spatially flat isotropic models…”

Section: Introductionmentioning

confidence: 99%