Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Jia, Ding

doi:10.48550/arxiv.2110.05953

Cited by 3 publications

(12 citation statements)

References 56 publications

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“…[24,25]. If the two points are on neighbouring hyperbolae, the angle is specified (in the convention of [25]) by a real part Re(ψ L± ) ∈ R and an imaginary contribution of either Im(ψ L+ ) = −π/2 (a choice advertised in [25]) or Im(ψ L− ) = +π/2 (which was used in [11]). As discussed in the introduction, the choice of sign determines which kind of causality violations are suppressed and which are enhanced.…”

Section: A On the Definition Of Angles In The Minkowskian Planementioning

confidence: 99%

“…In particular, it can be shown that only Lefschetz thimbles for critical points whose anti-thimbles (defined by (4.15) but with +∞) cut the original integration domain, contribute. Since by construction Lefschetz thimbles have the property that the real part of the exponent decays as quickly as possible along them, while the imaginary part remains constant, integrals of the form ∼ e W along them can become absolutely convergent, ease oscillatory behaviour for numerical simulations and be subject to Monte-Carlo simulations [3,5,11].…”

Section: Deforming the Integration Contour To Approximate The Lefsche...mentioning

confidence: 99%

“…The Lorentzian path integral is in particular important for quantum gravity [6][7][8][9][10][11]. Euclidean quantum gravity approaches use a formal Wick rotation, to justify a path integral based on the Euclidean gravity action, over Euclidean metrics.…”

Section: Introductionmentioning

confidence: 99%

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Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Asante¹,

Dittrich²,

Padua-Argüelles³

2021

Preprint

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For the construction of the Lorentzian path integral for gravity one faces two main questions: Firstly, what configurations to include, in particular whether to allow Lorentzian metrics that violate causality conditions. And secondly, how to evaluate a highly oscillatory path integral over unbounded domains. Relying on Picard-Lefschetz theory to address the second question for discrete Regge gravity, we will illustrate that it can also answer the first question. To this end we will define the Regge action for complexified variables and study its analytical continuation. Although there have been previously two different versions defined for the Lorentzian Regge action, we will show that the complex action is unique. More precisely, starting from the different definitions for the action one arrives at equivalent analytical extensions. The difference between the two Lorentzian versions is only realized along branch cuts which arise for a certain class of causality violating configurations.As an application we discuss the path integral describing a finite evolution step of the discretized deSitter universe. We will in particular consider an evolution from vanishing to finite scale factor, for which the path integral defines the no-boundary wave function.

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Section: A On the Definition Of Angles In The Minkowskian Planementioning

confidence: 99%

Section: Deforming the Integration Contour To Approximate The Lefsche...mentioning

confidence: 99%

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Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Asante¹,

Dittrich²,

Padua-Argüelles³

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Complex actions and causality violations: applications to Lorentzian quantum cosmology

Asante

Dittrich

Padua-Argüelles

2023

Class. Quantum Grav.

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For the construction of the Lorentzian path integral for gravity one faces two main questions: Firstly, what configurations to include, in particular whether to allow Lorentzian metrics that violate causality conditions. And secondly, how to evaluate a highly oscillatory path integral over unbounded domains. Relying on Picard-Lefschetz theory to address the second question for discrete Regge gravity, we will illustrate that it can also answer the first question. To this end we will define the Regge action for complexified variables and study its analytical continuation. Although there have been previously two different versions defined for the Lorentzian Regge action, we will show that the complex action is unique. More precisely, starting from the different definitions for the action one arrives at equivalent analytical extensions. The difference between the two Lorentzian versions is only realized along branch cuts which arise for a certain class of causality violating configurations. As an application we discuss the path integral describing a finite evolution step of the discretized deSitter universe. We will in particular consider an evolution from vanishing to finite scale factor, for which the path integral defines the no-boundary wave function.

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“…2 Recently a proposal for simulating Lorentzian QRC models (precisely speaking, complex generalizations of QRC) by applying the "generalized thimble algorithm" has been proposed [24]. 3 An improvement in applying the Gaussian quadrature to theories with continuous variables is described in [29].…”

Section: Introductionmentioning

confidence: 99%

Tensor network approach to 2d Lorentzian quantum Regge calculus

Ito¹,

Kadoh²,

Yuki³

2022

Preprint

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We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

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Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Cited by 3 publications

References 56 publications

Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Complex actions and causality violations: applications to Lorentzian quantum cosmology

Tensor network approach to 2d Lorentzian quantum Regge calculus

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