{"arxiv_id":"1904.13269","incoming":{"papers":9,"sentences":39,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"2012.02068","title":"Path integral renormalisation in loop quantum cosmology","url":"/paper/2012.02068","section":"Renormalised Hamiltonian from canonical quantisation","sentence":"The main content of the present paper will be to compute the analogue of [ref] in a coherent state path integral, i.e. to extract the renormlised Hamiltonian, canonical action, and path integral measure directly from a coherent state path integral based on the group quantisation given in section [ref] or equivalently the canonical theory in [ref] sketched in this section.","intent_p":0.97,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2012.02068","title":"Path integral renormalisation in loop quantum cosmology","url":"/paper/2012.02068","section":"Coherent states","sentence":"Given that we will choose the Hamiltonian of the system to be the linear combination of generators in [ref], we know that the time evolution operator \\(-i H t∈SU(1,1)\\), so that the entire time evolution of the coherent states can be computed by this very simple procedure [ref] , leading to [equation]","intent_p":0.92,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2012.02068","title":"Path integral renormalisation in loop quantum cosmology","url":"/paper/2012.02068","section":"Discussion","sentence":"The error made this way is very sensitive to taking the quantum numbers even slightly too large, i.e. if we peak the bounce volume on $2 v_m$ instead of $v_m$, we already overestimate the critical density by $87%$ as opposed to $100%$ at infinite bounce volume[To obtain these numbers, we simply evaluate the functions plotted in figure 1 of [ref] at $α≈0.268$.]. * While the model system considered in this paper as well as [ref] is very simple and not claimed to be an accurate reflection of our universe, it serves the purpose of illustrating the importance of renormalisation.","intent_p":0.88,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2012.02068","title":"Path integral renormalisation in loop quantum cosmology","url":"/paper/2012.02068","section":"Discussion","sentence":"An interesting observation which contrasts the canonical [ref] and path integral quantisations [ref] slightly is that the canonical Hamiltonian operator [ref] does not have any small volume corrections for $j=1/2$.","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":6,"quotes":[{"arxiv_id":"2012.02068","title":"Path integral renormalisation in loop quantum cosmology","url":"/paper/2012.02068","section":"Group quantisation, coarse graining map, and renormalised operators","sentence":"A more detailed review is given in [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"2109.10663","title":"The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology","url":"/paper/2109.10663","section":"Conclusions","sentence":"This looks very much like a very naïve renormalisation procedure and in future work it would be interesting to relate this to previous work in the context of coarse graining and renormalisation in loop quantum cosmology [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"2109.06843","title":"Tunneling dynamics in cosmological bounce models","url":"/paper/2109.06843","section":"Harmonic systems","sentence":"(See also [ref] for appearances of this algebra or related versions in quantum cosmology.) In these variables, the Hamiltonian [equation] is linear (again, up to the absolute value).","intent_p":0.9,"contests_p":null},{"arxiv_id":"2211.01268","title":"On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC","url":"/paper/2211.01268","section":"Further Future Directions","sentence":"For the case of cosmology, for instance, there has been recent effort e.g. in [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":28},"outgoing":{"papers":47,"sentences":94,"groups":[{"kind":"contests","label":"Contests","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1109.0499","title":"Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory","url":"/paper/1109.0499","section":"Conclusion","sentence":"The same criticism applies to computations within full loop quantum gravity (LQG) [ref] or related models [ref] , where one acts with the fundamental non-renormalised Hamiltonian on coarse quantum states, as well as to spin foam calculations in the same spirit, such as [ref] .","intent_p":0.42,"contests_p":0.72},{"arxiv_id":"1402.3155","title":"Quantum Reduced Loop Gravity: Semiclassical limit","url":"/paper/1402.3155","section":"Conclusion","sentence":"The same criticism applies to computations within full loop quantum gravity (LQG) [ref] or related models [ref] , where one acts with the fundamental non-renormalised Hamiltonian on coarse quantum states, as well as to spin foam calculations in the same spirit, such as [ref] .","intent_p":0.42,"contests_p":0.72},{"arxiv_id":"1410.5608","title":"A quantum reduction to Bianchi I models in loop quantum gravity","url":"/paper/1410.5608","section":"Conclusion","sentence":"The same criticism applies to computations within full loop quantum gravity (LQG) [ref] or related models [ref] , where one acts with the fundamental non-renormalised Hamiltonian on coarse quantum states, as well as to spin foam calculations in the same spirit, such as [ref] .","intent_p":0.42,"contests_p":0.72},{"arxiv_id":"1512.00713","title":"An embedding of loop quantum cosmology in (b, v) variables into a full theory context","url":"/paper/1512.00713","section":"Conclusion","sentence":"The same criticism applies to computations within full loop quantum gravity (LQG) [ref] or related models [ref] , where one acts with the fundamental non-renormalised Hamiltonian on coarse quantum states, as well as to spin foam calculations in the same spirit, such as [ref] .","intent_p":0.42,"contests_p":0.72},{"arxiv_id":"1706.09833","title":"Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics","url":"/paper/1706.09833","section":"Conclusion","sentence":"The same criticism applies to computations within full loop quantum gravity (LQG) [ref] or related models [ref] , where one acts with the fundamental non-renormalised Hamiltonian on coarse quantum states, as well as to spin foam calculations in the same spirit, such as [ref] 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verified.","intent_p":0.92,"contests_p":null},{"arxiv_id":"1811.02792","title":"Coarse graining as a representation change","url":"/paper/1811.02792","section":"Introduction","sentence":"While [ref] started from a classical Poisson algebra with this property, we are going to construct such operators directly on the loop quantum cosmology (LQC) Hilbert space in this paper.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1904.06149","title":"Protected $SL(2,\\mathbb{R})$ Symmetry in Quantum Cosmology","url":"/paper/1904.06149","section":"Conclusion","sentence":"This result extends previous investigations [ref] in which one started from a classical Poisson algebra with holonomy corrections.","intent_p":0.96,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":3,"sentences":4,"quotes":[{"arxiv_id":"1811.02792","title":"Coarse graining as a representation change","url":"/paper/1811.02792","section":"CVH algebra and regularisation","sentence":"The 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[ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1006.2451","title":"Dynamics for a 2-vertex Quantum Gravity Model","url":"/paper/1006.2451","section":"Quantising the CVH algebra and coarse graining","sentence":"Seminal papers about using an $𝔰𝔲(1,1)$ structure in LQC include [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"gr-qc/0206037","title":"Complexifier Coherent States for Quantum General Relativity","url":"/paper/gr-qc/0206037","section":"CVH algebra and regularisation","sentence":"For classical spatially flat homogeneous and isotropic cosmology, the CVH algebra is formed by the so called complexifier $C = v b$ (owing its name to [ref] ), the spatial volume $v$, and the gravitational part of the Hamiltonian constraint $H_g = - 1/2 v b^2$, where $b$ is proportional to the mean curvature.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1210.4504","title":"A new perspective on cosmology in Loop Quantum Gravity","url":"/paper/1210.4504","section":"Basics of the LQC 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