Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Asante, Seth K.; Dittrich, Bianca; Padua-Argüelles, José

doi:10.48550/arxiv.2112.15387

Cited by 11 publications

(29 citation statements)

References 37 publications

(99 reference statements)

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“…Evaluating the Lorentzian path integral involves a number of challenges shared across approaches. One question is which kind of configuration to allow in the path integral, i.e., whether to implement some strong notion of micro-causality or not [60,61]. Another question is how to effectively evaluate a path integral over highly oscillating amplitudes.…”

Section: Renormalization Groupmentioning

confidence: 99%

“…Another question is how to effectively evaluate a path integral over highly oscillating amplitudes. Recent work [61][62][63] spanning various approaches has employed Picard-Lefschetz methods based on a deformation of the integration contour into complexified configuration space. This brings up yet another question, namely which kind of complex metrics one should consider [64][65][66][67].…”

Section: Renormalization Groupmentioning

confidence: 99%

See 1 more Smart Citation

Frontiers of Quantum Gravity: shared challenges, converging directions

Boer¹,

Dittrich²,

Eichhorn³

et al. 2022

Preprint

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Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations of physics. Despite this common goal, the community of quantum gravity researchers is sometimes seen as divided into sub-communities working on different, mutually exclusive approaches. In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and interaction between traditionally distinct approaches. In this White Paper we discuss some of the common themes which have seen a growing interest from various directions, and argue that focusing on them will help the quantum gravity community as a whole towards shared objectives.

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Section: Renormalization Groupmentioning

confidence: 99%

Section: Renormalization Groupmentioning

confidence: 99%

Frontiers of Quantum Gravity: shared challenges, converging directions

Boer¹,

Dittrich²,

Eichhorn³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Real-time path integral [1] has recently been revisited both analytically [2][3][4] and numerically [5][6][7][8][9][10][11][12] for the interest of real-time dynamics in quantum theories. Especially in the numerical side, many developments have been made to tame the infamous sign problem (e.g., complex Langevin [13,14,5,6,15,16], contour deformation techniques including Lefschetz thimble methods [2,[17][18][19]3,20,7,21,22,8,9,[23][24][25][26][27][28][29][30]11], and tensor renormalization group [31][32][33][34][35][36][37][38][39]10]), which can enables us to investigate real-time qua...…”

Section: Introductionmentioning

confidence: 99%

Comment on the subtlety of defining real-time path integral in lattice gauge theories

Matsumoto¹

2022

Preprint

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Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to the Wilson action without divergences. We here show that the subtlety can be understood from the asymptotic expansion of the modified Bessel function, which has been discussed for path integral of compact variables in nonrelativistic quantum mechanics. The essential ingredient for defining the appropriate continuum theory is the iε prescription, which we show is applicable also for the Wilson action. It is here important that the iε should be implemented for both timelike and spacelike plaquettes. We then argue that such iε can be given a physical meaning that they remove singular paths having nontrivial winding for an infinitesimal time evolution that do not have corresponding paths in the continuum. Such point of view is only apparent in systems with compact variables as lattice gauge theories.

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“…This point of view will also help to important insights from ongoing work on domains of "allowable" complex metrics for a path integral of gravity[28,[33][34][35][36] and on applications of Picard-Lefschetz theory to it[37].…”

mentioning

confidence: 96%

The Spectral Geometry of de Sitter Space in Asymptotic Safety

Ferrero,

Reuter

2022

Preprint

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Within the functional renormalization group approach to Background Independent quantum gravity, we explore the scale dependent effective geometry of the de Sitter solution dS 4 . The investigation employs a novel approach whose essential ingredient is a modified spectral flow of the metric dependent d'Alembertian, or of similar hyperbolic kinetic operators. The corresponding one-parameter family of spectra and eigenfunctions encodes information about the nonperturbative backreaction of the dynamically gravitating vacuum fluctuations on the mean field geometry of the quantum spacetime. Used as a diagnostic tool, the power of the spectral flow method resides in its ability to identify the scale dependent subsets of field modes that supply the degrees of freedom which participate in the effective field theory description of the respective scale. A central result is that the ultraviolet of Quantum Einstein Gravity comprises far less effective degrees of freedom than predicted (incorrectly) by background dependent reasoning. The Lorentzian signature of dS 4 is taken into account by selecting a class of renormalization group trajectories which are known to apply to both the Euclidean and a Lorentzian version of the approach. Exploring the quantum spacetime's spatial geometry carried by physical fields, we find that 3-dimensional space disintegrates into a collection of coherent patches which individually can, but in their entirety cannot be described by one of the effective average actions occurring along the renormalization group trajectory. A natural concept of an entropy is introduced in order to quantify this fragmentation effect. Tentatively applied to the real Universe, surprising analogies to properties of the observed cosmic microwave background are uncovered. Furthermore, a set of distinguished field modes is found which, in principle, has the ability to transport information about the asymptotic fixed point regime from the ultraviolet, across almost the entire "scale history", to cosmological distances in the observed Universe.

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Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Cited by 11 publications

References 37 publications

Frontiers of Quantum Gravity: shared challenges, converging directions

Frontiers of Quantum Gravity: shared challenges, converging directions

Comment on the subtlety of defining real-time path integral in lattice gauge theories

The Spectral Geometry of de Sitter Space in Asymptotic Safety

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