Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity

Fabio D'Ambrosio

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Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity

Fabio D'Ambrosio

General Relativity and Quantum Cosmology · Submitted 14 Jan 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This method allows to systematically study amplitudes in the semi-classical regime of the theory and it sheds new light on the so-called cosine problem.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.11 · mentions code or data availability 0.02.

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Covariant Loop Quantum Gravity (CLQG) is a tentative background-independent and non-perturbative theory of quantum gravity which has emerged from a number of different research directions. Recently, this theory has been applied to the so-called Planck star model -- a particular model of stellar collapse in which non-perturbative quantum gravity effects play a predominant role. However, several obstacles have impeded progress in the investigation of this scenario. These obstacles range from conceptual issues, such as the question how to extract physical predictions from a background independent theory of quantum gravity, to computational problems due to a lack of systematic methods to evaluate CLQG transition amplitudes. This thesis addresses these problems directly. It contains an analysis of the Planck star model within the framework of CLQG, including a clarifying discussion on relevant conceptual issues. Moreover, a new approximation method for CLQG transition amplitudes is developed. This method allows to systematically study amplitudes in the semi-classical regime of the theory and it sheds new light on the so-called cosine problem.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Covariant Loop Quantum Gravity (CLQG) is a tentative background-independent and non-perturbative theory of quantum gravity which has emerged from a number of different research directions.	background 1.00	0.05	0.03	asserted 0.94
s1	Recently, this theory has been applied to the so-called Planck star model -- a particular model of stellar collapse in which non-perturbative quantum gravity effects play a predominant role.	background 1.00	0.13	0.03	asserted 1.00
s2	However, several obstacles have impeded progress in the investigation of this scenario.	background 0.63	0.07	0.02	asserted 1.00
s3	These obstacles range from conceptual issues, such as the question how to extract physical predictions from a background independent theory of quantum gravity, to computational problems due to a lack of systematic methods to evaluate CLQG transition amplitudes.	gap 0.63	0.05	0.03	asserted 1.00
s4	This thesis addresses these problems directly.	contribution 0.98	0.77	0.05	asserted 1.00
s5	It contains an analysis of the Planck star model within the framework of CLQG, including a clarifying discussion on relevant conceptual issues.	contribution 1.00	0.90	0.11	asserted 0.99
s6	Moreover, a new approximation method for CLQG transition amplitudes is developed.	contribution 0.90	0.95	0.20	asserted 1.00
s7	This method allows to systematically study amplitudes in the semi-classical regime of the theory and it sheds new light on the so-called cosine problem.	contribution 0.35	0.92	0.35	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.97 · evidence from proof or derivation 0.96.

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Original abstract

Covariant Loop Quantum Gravity (CLQG) is a tentative background-independent and non-perturbative theory of quantum gravity which has emerged from a number of different research directions. Recently, this theory has been applied to the so-called Planck star model -- a particular model of stellar collapse in which non-perturbative quantum gravity effects play a predominant role. However, several obstacles have impeded progress in the investigation of this scenario. These obstacles range from conceptual issues, such as the question how to extract physical predictions from a background independent theory of quantum gravity, to computational problems due to a lack of systematic methods to evaluate CLQG transition amplitudes. This thesis addresses these problems directly. It contains an analysis of the Planck star model within the framework of CLQG, including a clarifying discussion on relevant conceptual issues. Moreover, a new approximation method for CLQG transition amplitudes is developed. This method allows to systematically study amplitudes in the semi-classical regime of the theory and it sheds new light on the so-called cosine problem.

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4 arXiv papers cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Uses its method or tool 1 paper

Following the strategy of [ref] , we restrict the validity of the amplitude [ref] to a single period over $T$.

Numerical approach to the black-to-white hole transition · The numerical algorithm · 0.93

Cites it as background 1 paper

For instance, $Q_αμν$ is also a measure for how the angle[For a definition of angles in Lorentzian geometries of arbitrary dimension see for instance [ref] .] between two vectors change.

Review on $f(Q)$ Gravity · Non-Metricity · 0.86

What it cites · 204 sentences without a confident label

Builds on 1 paper

For the Lorentzian case, we generalize a definition given by Barrett and Foxon [ref] for $1+1$ dimensional Minkowski space and we clarify certain aspects of the construction which are important for applications in spin foams and which are a common source of confusion.

Semi-Classical Limits of Simplicial Quantum Gravity · On Euclidean and Lorentzian Angles · 0.99

Uses the method or tool of 11 papers

The strategy employed in [ref] is to use the holomorphic transition amplitude [ref] in its general form rather than in its very specialized form derived in [ref] .

Geometry Transition in Covariant Loop Quantum Gravity · CLQG Computation of the Black Hole to White Hole Transition · 0.84
The strategy employed in [ref] is to use the holomorphic transition amplitude [ref] in its general form rather than in its very specialized form derived in [ref] .

Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time · CLQG Computation of the Black Hole to White Hole Transition · 0.84
Following [ref] we restrict the domain of integration to [equation] for some $T>0$ and then we consider the matrix elements [equation] where $|s⟩$, $|s'⟩$ are $s$-knot states.

The projector on physical states in loop quantum gravity · From the canonical Theory to Spin Foams · 0.94

Uses data or values from 1 paper

If we use the boundary data specified in [ref] , then we only need to consider the four links which connect the top nodes to the bottom nodes in Figure [ref].

Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time · Estimation of the Bounce Time from CLQG · 0.86

Compares with 6 papers

Hence, the vector $v$ reduces to the components $v_ℓ= r_ℓ= ξ_ℓ- θ_ℓ$ and, when restricted to the appropriate subspaces, the vector $V$ and the matrices $K$, $M$, $H$ assume the simple forms [equation] It then follows immediately that [equation] Since $S_(a_ℓ, n_) = 0$ due to the above assumptions (it only contains bulk quantities), we finally get from [ref] [equation] This is exactly the same result derived in chapter [ref] and reported in [ref] !

Geometry Transition in Covariant Loop Quantum Gravity · Application to the Black Hole to White Hole Transition · 0.83
Hence, the vector $v$ reduces to the components $v_ℓ= r_ℓ= ξ_ℓ- θ_ℓ$ and, when restricted to the appropriate subspaces, the vector $V$ and the matrices $K$, $M$, $H$ assume the simple forms [equation] It then follows immediately that [equation] Since $S_(a_ℓ, n_) = 0$ due to the above assumptions (it only contains bulk quantities), we finally get from [ref] [equation] This is exactly the same result derived in chapter [ref] and reported in [ref] !

Characteristic Time Scales for the Geometry Transition of a Black Hole to a White Hole from Spinfoams · Application to the Black Hole to White Hole Transition · 0.83
Plugging [ref] into [ref] and changing from a product over vertices $∈$ to an equivalent product over edges $∈$ brings the bulk face amplitude into the form [equation] As in [ref] and [ref] we introduced the rescaled measure [equation] and a Lagrangian $L_[g_, z_]$ associated to internal faces: [equation] If the $2$-complex had no boundary, i.e. if $Γ= ∅$, then the CLQG propagator in its path integral form would read [equation] which is precisely the result obtained in [ref] by different group theoretical methods.

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory · The Propagator on a $2$-Complex without Boundary · 0.90

Cites as support 2 papers

Although the results of [ref] guarantee that the Hessian is non-degenerate for Lorentzian critical points and the above expression is therefore well-defined.

The hessian in spin foam models · CLQG Computation of the Black Hole to White Hole Transition · 0.99
It can be shown [ref] that because of the exponential damping factor, there is always one critical point which dominates over the others.

Characteristic Time Scales for the Geometry Transition of a Black Hole to a White Hole from Spinfoams · CLQG Computation of the Black Hole to White Hole Transition · 0.98

Cites as background 46 papers

In [ref] , Thiemann studied two different complexifier operators defined on the Hilbert space $L_2[SU(2)^L/SU(2)^N]_Γ$ and introduced candidate coherent states for LQG.

Gauge Field Theory Coherent States (GCS) : I. General Properties · Thiemann's Heat Kernel States · 0.80
See again [ref] for a detailed and didactical explanation.

Geometry Transition in Covariant Loop Quantum Gravity · The Classical Limit and the Emergence of Geometry · 0.87
We refer the interested reader to the extensive literature [ref] for the details.

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory · The Classical Limit and the Emergence of Geometry · 1.00

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