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The gravitational path integral from an observer’s point of view

Abdalla, Ahmed I., Antonini, Stefano, Iliesiu, Luca V., Levine, Adam·2025·Journal of High Energy Physics
DOI 10.1007/jhep05(2025)059
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Abstract

A bstract: One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with $${G}_{N}^{-1}$$ . Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

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Figure 1 Our proposal for the gravitational path integral in the presence of an observer. The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap ⟨ ψ i | ψ j ⟩ n . This rule can be seen as an additional boundary condition to impose when summing over geometries. (a) The overlap ⟨ ψ i | ψ j ⟩ between two closed universe states in pure JT gravity is unaffected by our new rules. (b) The square of an overlap |⟨ ψ i | ψ j ⟩| 2 between closed universe states. The gravitational path integral sums over all possible geometries satisfying the boundary conditions at the asymptotic boundaries and at the worldline of the observer. We depict here the leading disconnected contribution and the first subleading term, a genus-zero connected geometry.
Figure 1 Our proposal for the gravitational path integral in the presence of an observer. The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap ⟨ ψ i | ψ j ⟩ n . This rule can be seen as an additional boundary condition to impose when summing over geometries. (a) The overlap ⟨ ψ i | ψ j ⟩ between two closed universe states in pure JT gravity is unaffected by our new rules. (b) The square of an overlap |⟨ ψ i | ψ j ⟩| 2 between closed universe states. The gravitational path integral sums over all possible geometries satisfying the boundary conditions at the asymptotic boundaries and at the worldline of the observer. We depict here the leading disconnected contribution and the first subleading term, a genus-zero connected geometry.CC-BY · From the PDF
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Figure 2 (Left) A Lorentzian Big Bang-Big Crunch closed universe with a Cauchy slice of maximal length b (depicted in blue). (Right) Its Euclidean counterpart has two AdS asymptotic boundaries connected by a Euclidean wormhole. The geodesic slice of minimal length b is identical to the maximal slice in Lorentzian signature. This length is vanishingly small on-shell when the wormhole is not supported by matter and is finite in the presence of matter.
Figure 2 (Left) A Lorentzian Big Bang-Big Crunch closed universe with a Cauchy slice of maximal length b (depicted in blue). (Right) Its Euclidean counterpart has two AdS asymptotic boundaries connected by a Euclidean wormhole. The geodesic slice of minimal length b is identical to the maximal slice in Lorentzian signature. This length is vanishingly small on-shell when the wormhole is not supported by matter and is finite in the presence of matter.CC-BY · From the PDF
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Figure 3 The integration contour needed to calculate the Hilbert space dimension consists of the large defining contour of the resolvent C ∞ and a small contour C 0 used to exclude the contributions from zero eigenvalues of the Gram matrix.
Figure 3 The integration contour needed to calculate the Hilbert space dimension consists of the large defining contour of the resolvent C ∞ and a small contour C 0 used to exclude the contributions from zero eigenvalues of the Gram matrix.CC-BY · From the PDF
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Figure 4 Overlap between an asymptotic closed universe state | β, ∆ ( i ) O ⟩ and a state defined on the closed minimal geodesic (depicted in green) | b, ∆ ( i ) O , u ⟩ . Left: the overlap on the Euclidean cylinder. The state on the minimal closed geodesic is labeled by the length b of the closed minimal geodesic and the length u of a geodesic segment wrapping the cylinder once and intersecting the observer's worldline perpendicularly at both ends. Right: the cylinder can be cut along the observer's worldline and embedded in the Poincar´ e disk (depicted in black), with the two red lines identified. The contribution of this geometry to the path integral can be decomposed into a Hartle-Hawking wavefunction ϕ β ( ℓ i ), with ℓ i the length of a geodesic starting and ending at the insertion of the observer on the asymptotic boundary, and a quadrilateral.
Figure 4 Overlap between an asymptotic closed universe state | β, ∆ ( i ) O ⟩ and a state defined on the closed minimal geodesic (depicted in green) | b, ∆ ( i ) O , u ⟩ . Left: the overlap on the Euclidean cylinder. The state on the minimal closed geodesic is labeled by the length b of the closed minimal geodesic and the length u of a geodesic segment wrapping the cylinder once and intersecting the observer's worldline perpendicularly at both ends. Right: the cylinder can be cut along the observer's worldline and embedded in the Poincar´ e disk (depicted in black), with the two red lines identified. The contribution of this geometry to the path integral can be decomposed into a Hartle-Hawking wavefunction ϕ β ( ℓ i ), with ℓ i the length of a geodesic starting and ending at the insertion of the observer on the asymptotic boundary, and a quadrilateral.CC-BY · From the PDF
Figure 5 Non-perturbative corrections to the overlap ⟨ b, ∆ ( i ) O , u | β, ∆ ( j ) O ⟩ . The geodesic slice of length b is depicted in green. Any higher-genus geometry contributing to the overlap can be decomposed into a genus-zero quadrilateral similar to Figure 4 and a region with a higher genus homologous to the boundary. The contribution of geometries with higher topology is then encoded in the Hartle-Hawking wavefunction.
Figure 5 Non-perturbative corrections to the overlap ⟨ b, ∆ ( i ) O , u | β, ∆ ( j ) O ⟩ . The geodesic slice of length b is depicted in green. Any higher-genus geometry contributing to the overlap can be decomposed into a genus-zero quadrilateral similar to Figure 4 and a region with a higher genus homologous to the boundary. The contribution of geometries with higher topology is then encoded in the Hartle-Hawking wavefunction.CC-BY · From the PDF
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Figure 7 Path integral preparing a generic closed universe state | ψ i ⟩ in the presence of an observer and a matter insertion labeled by i . Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of a matter operator with flavor i and scaling dimension ∆ m at the asymptotic boundary. The insertions are at antipodal points. Right: the gravitational path integral prepares a state for the closed universe satisfying these boundary conditions. We indicate here the energies s 1 and s 2 of the patches to the left and right of the observer. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.1) and (4.2).
Figure 7 Path integral preparing a generic closed universe state | ψ i ⟩ in the presence of an observer and a matter insertion labeled by i . Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of a matter operator with flavor i and scaling dimension ∆ m at the asymptotic boundary. The insertions are at antipodal points. Right: the gravitational path integral prepares a state for the closed universe satisfying these boundary conditions. We indicate here the energies s 1 and s 2 of the patches to the left and right of the observer. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.1) and (4.2).CC-BY · From the PDF
Figure 8 Genus-zero pinwheel geometry contributing to the n = 3 moment of an overlap ⟨ ψ i | ψ j ⟩⟨ ψ j | ψ k ⟩⟨ ψ k | ψ i ⟩ (no sum over indices). The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets.
Figure 8 Genus-zero pinwheel geometry contributing to the n = 3 moment of an overlap ⟨ ψ i | ψ j ⟩⟨ ψ j | ψ k ⟩⟨ ψ k | ψ i ⟩ (no sum over indices). The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets.CC-BY · From the PDF
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Figure 9 Path integral preparing a state | ψ ii ′ ⟩ for the two-sided black hole in the presence of an observer and matter insertions to the right and left of the observer labeled by i and i ′ . Every boundary segment in the preparation of a state is taken to have length β/ 8. Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of matter operators with flavors i and i ′ and scaling dimension ∆ m at the asymptotic boundary. Right: the gravitational path integral prepares a state for the two-sided black hole satisfying these boundary conditions. We indicate here the energies s 1 , s 2 , s 3 , s 4 of the four patches. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.11) and (4.12).
Figure 9 Path integral preparing a state | ψ ii ′ ⟩ for the two-sided black hole in the presence of an observer and matter insertions to the right and left of the observer labeled by i and i ′ . Every boundary segment in the preparation of a state is taken to have length β/ 8. Left: boundary conditions for the path integral, with a worldline for the observer (depicted in red) and the insertion of matter operators with flavors i and i ′ and scaling dimension ∆ m at the asymptotic boundary. Right: the gravitational path integral prepares a state for the two-sided black hole satisfying these boundary conditions. We indicate here the energies s 1 , s 2 , s 3 , s 4 of the four patches. We omit these labels in the rest of the Figures in this section, but the same convention is used in all geometries, leading to equations (4.11) and (4.12).CC-BY · From the PDF
Figure 10 Genus n -1 geometries with n boundaries contributing to the n -th moment of an overlap in the two-sided black hole in the presence of an observer. The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets. Geodesics do not intersect in these leading, connected contributions. (a) Genus g = 1, 2-boundary geometry contributing to the square of an overlap |⟨ ψ jj ′ | ψ ii ′ ⟩| 2 . (b) Genus g = 2, 3-boundary geometry contributing to the n = 3 moment of an overlap ⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | ψ kk ′ ⟩⟨ ψ kk ′ | ψ jj ′ ⟩ (no sum over indices).
Figure 10 Genus n -1 geometries with n boundaries contributing to the n -th moment of an overlap in the two-sided black hole in the presence of an observer. The observer's worldlines (depicted in red) must connect between a bra and the corresponding ket. Matter geodesics (depicted in green) can connect between arbitrary bras and kets. Geodesics do not intersect in these leading, connected contributions. (a) Genus g = 1, 2-boundary geometry contributing to the square of an overlap |⟨ ψ jj ′ | ψ ii ′ ⟩| 2 . (b) Genus g = 2, 3-boundary geometry contributing to the n = 3 moment of an overlap ⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | ψ kk ′ ⟩⟨ ψ kk ′ | ψ jj ′ ⟩ (no sum over indices).CC-BY · From the PDF
Figure 11 The genus n -1, n -boundary geometry contributing to the n -th moment of an overlap can be obtained by gluing together two genus-0 pinwheel geometries with n boundaries. Here we depict the pinwheels and the resulting glued geometry for n = 3. Each boundary of the pinwheels is composed of a segment of asymptotic boundary and a segment of observer's worldline. The two pinwheels are glued together along the observer's worldlines as depicted.
Figure 11 The genus n -1, n -boundary geometry contributing to the n -th moment of an overlap can be obtained by gluing together two genus-0 pinwheel geometries with n boundaries. Here we depict the pinwheels and the resulting glued geometry for n = 3. Each boundary of the pinwheels is composed of a segment of asymptotic boundary and a segment of observer's worldline. The two pinwheels are glued together along the observer's worldlines as depicted.CC-BY · From the PDF
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Figure 12 Euclidean diagrams showing the two-point function of a scalar field ϕ , dressed to the worldline of the observer. The figure on the right is obtained by cutting the figure on the left along the observer's worldline, embedding the resulting geometry in the Poincar´ e disk (depicted in black), and then identifying the two red geodesics of length ℓ in the right diagram. We give an example of the worldline connecting the two operator insertions that winds once around the cylinder, which we show in dark green in both diagrams. The light green circle (left) and line (right) represent the shortest closed geodesic on the geometry, while the blue line (only shown on the right) is the shortest geodesic (not closed) perpendicular to the worldline of the observer on both ends. To evaluate the two-point function in the Lorentzian closed universe we perform the analytic continuation τ 1 , 2 = -it 1 , 2 .
Figure 12 Euclidean diagrams showing the two-point function of a scalar field ϕ , dressed to the worldline of the observer. The figure on the right is obtained by cutting the figure on the left along the observer's worldline, embedding the resulting geometry in the Poincar´ e disk (depicted in black), and then identifying the two red geodesics of length ℓ in the right diagram. We give an example of the worldline connecting the two operator insertions that winds once around the cylinder, which we show in dark green in both diagrams. The light green circle (left) and line (right) represent the shortest closed geodesic on the geometry, while the blue line (only shown on the right) is the shortest geodesic (not closed) perpendicular to the worldline of the observer on both ends. To evaluate the two-point function in the Lorentzian closed universe we perform the analytic continuation τ 1 , 2 = -it 1 , 2 .CC-BY · From the PDF
Figure 13 Two frontal views of the closed universe in Lorentzian signature. The observer's worldline is depicted in red and the maximal Cauchy slice of length b is depicted in green. We insert a matter insertion at time t 1 = 0, defined by where the observer intersects this Cauchy slice. Another matter insertion is place sometime later along the observer's worldline. ( Left ) Left and right null rays emanating from the first matter insertion are shown in brown. Each time the second operator insertion is placed at the intersection of these null rays with the worldline of the observer, the two-point function on a fixed background diverges. ( Right ) Generically, an infinite number of winding geodesics contribute to the twopoint function. A timelike geodesic along the observer's worldline is drawn in purple, a winding spacelike geodesic is drawn in blue, and a null winding geodesic is shown in brown.
Figure 13 Two frontal views of the closed universe in Lorentzian signature. The observer's worldline is depicted in red and the maximal Cauchy slice of length b is depicted in green. We insert a matter insertion at time t 1 = 0, defined by where the observer intersects this Cauchy slice. Another matter insertion is place sometime later along the observer's worldline. ( Left ) Left and right null rays emanating from the first matter insertion are shown in brown. Each time the second operator insertion is placed at the intersection of these null rays with the worldline of the observer, the two-point function on a fixed background diverges. ( Right ) Generically, an infinite number of winding geodesics contribute to the twopoint function. A timelike geodesic along the observer's worldline is drawn in purple, a winding spacelike geodesic is drawn in blue, and a null winding geodesic is shown in brown.CC-BY · From the PDF
Figure 14 The left-most diagram illustrates how if the observer and particle jump in both at early times, the geodesic slice for the wormhole is shrinking. This leads to a large relative boost between the observer and the particle and a correspondingly high energy collision. If both insertions happen far in the future (center diagram), then the observer and particle experience a growing wormhole length and only a minor collision. In the right-most diagram, we illustrate how the boost symmetry of the thermofield double can be used to move one of the insertions down to T = 0. In this work we choose to fix V at T = 0 on the left and vary the time that the observer jumps in. The above figure is reproduced from Figure 1 of [38].
Figure 14 The left-most diagram illustrates how if the observer and particle jump in both at early times, the geodesic slice for the wormhole is shrinking. This leads to a large relative boost between the observer and the particle and a correspondingly high energy collision. If both insertions happen far in the future (center diagram), then the observer and particle experience a growing wormhole length and only a minor collision. In the right-most diagram, we illustrate how the boost symmetry of the thermofield double can be used to move one of the insertions down to T = 0. In this work we choose to fix V at T = 0 on the left and vary the time that the observer jumps in. The above figure is reproduced from Figure 1 of [38].CC-BY · From the PDF
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Figure 15 The left figure illustrates the geometry obtained upon cutting the wormhole in (6.36) along the dashed line. The resulting geometry corresponds to the bra-ket to bra-ket wormhole contributing to the square of ⟨ n, s L , s R | V (0) O O ( -T ) ⟩ . In the right figure, the | n, s L , s R ⟩ boundary conditions are replaced by (an integral of) asymptotic boundary segments given by the state | s L , s R , V O O s ⟩ .
Figure 15 The left figure illustrates the geometry obtained upon cutting the wormhole in (6.36) along the dashed line. The resulting geometry corresponds to the bra-ket to bra-ket wormhole contributing to the square of ⟨ n, s L , s R | V (0) O O ( -T ) ⟩ . In the right figure, the | n, s L , s R ⟩ boundary conditions are replaced by (an integral of) asymptotic boundary segments given by the state | s L , s R , V O O s ⟩ .CC-BY · From the PDF
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Figure 16 Examples of two-dimensional boundary configurations relevant for studying dressed observables in a closed universe (left figures) or in a two-sided black hole (right figures). The undeformed CFT is placed on all tori (asymptotic boundaries); a future task is to find the precise deformation of the CFT to be placed on the red cylinders (boundaries of the observer worldvolumes). The first figure in each set assumes that the worldvolume of each observer is bounded by the thin red cylinder, while the second figure in each set assumes that the observer is circularly symmetric and their worldvolume is bounded by the two red cylinders. The latter case is related through dimensional reduction to the analysis performed in this paper.
Figure 16 Examples of two-dimensional boundary configurations relevant for studying dressed observables in a closed universe (left figures) or in a two-sided black hole (right figures). The undeformed CFT is placed on all tori (asymptotic boundaries); a future task is to find the precise deformation of the CFT to be placed on the red cylinders (boundaries of the observer worldvolumes). The first figure in each set assumes that the worldvolume of each observer is bounded by the thin red cylinder, while the second figure in each set assumes that the observer is circularly symmetric and their worldvolume is bounded by the two red cylinders. The latter case is related through dimensional reduction to the analysis performed in this paper.CC-BY · From the PDF
Figure 17 The Euclidean preparation (bottom half) and subsequent Lorentzian evolution (top half) of a de Sitter state | a, K, ∆ ( i ) O ⟩ specified by the length a and extrinsic curvature K of an initial slice at Euclidean time τ = τ i where the observer is inserted. The Lorentzian part of the evolution from the Euclidean sphere's equator at τ = 0 (depicted in blue) yields Lorentzian dS 2 , with a spacelike asymptotic boundary at Lorentzian time t → ∞ . Our set of states | a, K, ∆ ( i ) O ⟩ includes (but is not limited to) the smooth Hartle-Hawking no-boundary state.
Figure 17 The Euclidean preparation (bottom half) and subsequent Lorentzian evolution (top half) of a de Sitter state | a, K, ∆ ( i ) O ⟩ specified by the length a and extrinsic curvature K of an initial slice at Euclidean time τ = τ i where the observer is inserted. The Lorentzian part of the evolution from the Euclidean sphere's equator at τ = 0 (depicted in blue) yields Lorentzian dS 2 , with a spacelike asymptotic boundary at Lorentzian time t → ∞ . Our set of states | a, K, ∆ ( i ) O ⟩ includes (but is not limited to) the smooth Hartle-Hawking no-boundary state.CC-BY · From the PDF
Figure 18 The gravitational path integral in the presence of an observer for de Sitter spacetime. A state is defined in terms of the length a and extrinsic curvature K of an initial slice where we insert the observer with scaling dimension ∆ O . The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap. (a) The overlap ⟨ a ′ , K ′ | a, K ⟩ between two states. (b) The square of an overlap |⟨ a ′ , K ′ | a, K ⟩| 2 in the presence of an observer. The variance of the overlap is given by the connected geometry on the right, namely a sphere with four holes, and is therefore O ( e -2 S 0 ). This suggests a Hilbert space dimension dim ( H rel non-pert ) = O ( e 2 S 0 ). We plan to explicitly compute this dimension in future work.
Figure 18 The gravitational path integral in the presence of an observer for de Sitter spacetime. A state is defined in terms of the length a and extrinsic curvature K of an initial slice where we insert the observer with scaling dimension ∆ O . The worldline of the observer (depicted in red) must connect a bra and the corresponding ket when computing moments of an overlap. (a) The overlap ⟨ a ′ , K ′ | a, K ⟩ between two states. (b) The square of an overlap |⟨ a ′ , K ′ | a, K ⟩| 2 in the presence of an observer. The variance of the overlap is given by the connected geometry on the right, namely a sphere with four holes, and is therefore O ( e -2 S 0 ). This suggests a Hilbert space dimension dim ( H rel non-pert ) = O ( e 2 S 0 ). We plan to explicitly compute this dimension in future work.CC-BY · From the PDF
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Figure 19 Boundary conditions for a closed universe state prepared by the insertion of the observer, a matter operator of flavor i , and operators k l = e -β l H l and k r = e -β r H r to the left and right of the observer. The insertion of k l and k r in a state with boundary length β/ 2 to the left and right of the observer (left picture) is equivalent to a state with boundary length β/ 2 + β l to the left of the observer and β/ 2 + β r to the right of the observer (right picture).
Figure 19 Boundary conditions for a closed universe state prepared by the insertion of the observer, a matter operator of flavor i , and operators k l = e -β l H l and k r = e -β r H r to the left and right of the observer. The insertion of k l and k r in a state with boundary length β/ 2 to the left and right of the observer (left picture) is equivalent to a state with boundary length β/ 2 + β l to the left of the observer and β/ 2 + β r to the right of the observer (right picture).CC-BY · From the PDF
Figure 20 Genus-zero pinwheel geometry contributing to the n = 2 term ⟨ ψ l | ψ i ⟩⟨ ψ i | ψ j ⟩⟨ ψ j | k l k r | ψ l ⟩ on the right hand side of equation (C.4).
Figure 20 Genus-zero pinwheel geometry contributing to the n = 2 term ⟨ ψ l | ψ i ⟩⟨ ψ i | ψ j ⟩⟨ ψ j | k l k r | ψ l ⟩ on the right hand side of equation (C.4).CC-BY · From the PDF
Figure 21 Boundary conditions for a two-sided black hole state prepared by the insertion of the observer, two matter operators to the left and right of the observer, and operators k l = e -β l H l , k r = e -β r H r , k L = e -β L H L , k R = e -β R H R . The insertion of k l , k r , k L , k R in a state with every boundary segment of length β/ 8 (left picture) is equivalent to a state with boundary segments of length β/ 8 + β l , β/ 8 + β r , β/ 8 + β L , and β/ 8 + β R (right picture).
Figure 21 Boundary conditions for a two-sided black hole state prepared by the insertion of the observer, two matter operators to the left and right of the observer, and operators k l = e -β l H l , k r = e -β r H r , k L = e -β L H L , k R = e -β R H R . The insertion of k l , k r , k L , k R in a state with every boundary segment of length β/ 8 (left picture) is equivalent to a state with boundary segments of length β/ 8 + β l , β/ 8 + β r , β/ 8 + β L , and β/ 8 + β R (right picture).CC-BY · From the PDF
Figure 22 Genus g = 2 geometry contributing to the n = 2 term ⟨ ψ ll ′ | ψ jj ′ ⟩⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | k L k l k R k r | ψ ll ′ ⟩ on the right hand side of equation (C.13).
Figure 22 Genus g = 2 geometry contributing to the n = 2 term ⟨ ψ ll ′ | ψ jj ′ ⟩⟨ ψ jj ′ | ψ ii ′ ⟩⟨ ψ ii ′ | k L k l k R k r | ψ ll ′ ⟩ on the right hand side of equation (C.13).CC-BY · From the PDF

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Metadata

Authors
Abdalla, A. I., Antonini, S., Iliesiu, L. V., & Levine, A.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2025-05-07
Volume
2025
Issue
5
ISSN
1029-8479
DOI
10.1007/jhep05(2025)059
Cited by
30
References
13
Language
en
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CoChat. (2026). Citation check: The gravitational path integral from an observer’s point of view. https://app.cochat.ai/papers/10.1007/jhep05(2025)059
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Abdalla, A. I., Antonini, S., Iliesiu, L. V., & Levine, A. (2025). The gravitational path integral from an observer’s point of view. Journal of High Energy Physics. https://doi.org/10.1007/jhep05(2025)059