Causal set d'Alembertians for various dimensions

Dowker, Fay; Glaser, Lisa

doi:10.1088/0264-9381/30/19/195016

Cited by 70 publications

(154 citation statements)

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“…The action we shall use, the Benincasa-Dowker action, was introduced in [10]. For a causal set C with n elements, it takes the general form [11,12] 1…”

Section: Causal Set Path Integralsmentioning

confidence: 99%

Suppression of non-manifold-like sets in the causal set path integral

Loomis

Carlip

2017

Class. Quantum Grav.

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While it is possible to build causal sets that approximate spacetime manifolds, most causal sets are not at all manifold-like. We show that a Lorentzian path integral with the Einstein-Hilbert action has a phase in which one large class of non-manifold-like causal sets is strongly suppressed, and suggest a direction for generalization to other classes. While we cannot yet show our argument holds for all non-manifold-like sets, our results make it plausible that the path integral might lead to emergent manifold-like behavior with no need for further conditions. *

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“…The action we shall use, the Benincasa-Dowker action, was introduced in [10]. For a causal set C with n elements, it takes the general form [11,12] 1…”

Section: Causal Set Path Integralsmentioning

confidence: 99%

Suppression of non-manifold-like sets in the causal set path integral

Loomis

Carlip

2017

Class. Quantum Grav.

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“…for causets derived by sprinkling M 2 ). The expression introduced in [2] was generalized to D = 4 dimensions in [3] and recently to arbitrary D in [4,5].…”

Section: Jhep06(2014)024mentioning

confidence: 99%

“…We will show in section 3.1 that the "spectrum" of (4) ρ , as defined by (4) ρ e ip·x = g (4) ρ (p)e ip·x , is given by…”

Section: Dmentioning

confidence: 99%

“…Many properties of the 2D function g (2) ρ (p) carry over to g (4) ρ (p) . For timelike p, the value of g (4) ρ (p) above/below the branch cut corresponds to past/future-directed momenta, and it changes to its complex conjugate across the cut. Also, g (4) ρ is real for spacelike momenta.…”

Section: Dmentioning

confidence: 99%

“…For timelike p, the value of g (4) ρ (p) above/below the branch cut corresponds to past/future-directed momenta, and it changes to its complex conjugate across the cut. Also, g (4) ρ is real for spacelike momenta. Figure 3(b) shows the behaviour of g (4) ρ (p) for real momenta.…”

Section: Dmentioning

confidence: 99%

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Generalized causal set d’Alembertians

Aslanbeigi

Saravani

Sorkin

2014

J. High Energ. Phys.

105

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We introduce a family of generalized d'Alembertian operators in D-dimensionalMinkowski spacetimes M D which are manifestly Lorentz-invariant, retarded, and non-local, the extent of the nonlocality being governed by a single parameter ρ. The prototypes of these operators arose in earlier work as averages of matrix operators meant to describe the propagation of a scalar field in a causal set. We generalize the original definitions to produce an infinite family of "Generalized Causet Box (GCB) operators" parametrized by certain coefficients {a, b n }, and we derive the conditions on the latter needed for the usual d'Alembertian to be recovered in the infrared limit. The continuum average of a GCB operator is an integral operator in M D , and it is these continuum operators that we mainly study. To that end, we compute their action on plane waves, or equivalently their Fourier transforms g(p) [p being the momentum-vector]. For timelike p, g(p) has an imaginary part whose sign depends on whether p is past or future-directed. For small p, g(p) is necessarily proportional to p · p, but for large p it becomes constant, raising the possibility of a genuinely Lorentzian perturbative regulator for quantum field theory in M D . We also address the question of whether or not the evolution defined by the GCB operators is stable, finding evidence that the original 4D causal set d'Alembertian is unstable, while its 2D counterpart is stable.

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Cosmology of Quantum Gravities

Calcagni

2017

Classical and Quantum Cosmology

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Causal set d'Alembertians for various dimensions

Abstract: We propose, for dimension d, a discrete Lorentz invariant operator on scalar fields that approximates the Minkowski spacetime scalar d'Alembertian. For each dimension, this gives rise to a scalar curvature estimator for causal sets, and thence to a proposal for a causal set action.

Cited by 70 publications

References 6 publications

Suppression of non-manifold-like sets in the causal set path integral

Suppression of non-manifold-like sets in the causal set path integral

Generalized causal set d’Alembertians

Cosmology of Quantum Gravities

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