Building a path-integral calculus: a covariant discretization approach

Cugliandolo, Leticia F.; Lecomte, Vivien; Wijland, Frédéric van

doi:10.1088/1751-8121/ab3ad5

Cited by 29 publications

(32 citation statements)

References 74 publications

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“…It is not the case with fractional spacetime, where correct fractional Path Integrals can be defined as well as uncertainty principles [436]. In a discrete environment, they can also maintain their Lorentz covariance [498].…”

Section: A Case For a Discrete Spacetime In U M F ?mentioning

confidence: 99%

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Maes¹

2020

Preprint

217

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We start from a hypothetical multi-fold universe U_{MF}}, where the propagation of everything is slower or equal to the speed of light and where entanglement extends the set of paths available to Path Integrals. This multi-fold mechanism enables EPR (Einstein-Podolsky-Rosen) “spooky actions at distance” to result from local interactions in the resulting folds. It produces gravity-like attractive effective potentials in the spacetime, between entangled entities, that are caused by the curvature of the folds. When quantized, multi-folds correspond to gravitons and they are enablers of EPR entanglement. Gravity emerges non-perturbative and covariant from EPR entanglement between virtual particles surrounding an entity.In U_{MF}, we encounter mechanisms that predict gravity fluctuations when entanglement is present, including in macroscopic entanglements. Besides providing a new perspective on quantum gravity, when added to the Standard Model and Standard Cosmology, U_{MF} can contribute explanations of several open questions and challenges. It also clarifies some relationships and challenges met by other quantum gravity models and Theories of Everything. It leads to suggestions for these works.We also reconstruct the spacetime of U_{MF}, starting from the random walks of particles in an early spacetime. U_{MF} now appears as a noncommutative, discrete, yet Lorentz symmetric, spacetime that behaves roughly 2-Dimensional at Planck scales, when it is a graph of microscopic Planck size black holes on a random walk fractal structure left by particles that can also appear as also microscopic black holes. Of course, at larger scales, spacetime appears 4-D, where we are able to explain curvature and recover Einstein’s General Relativity. We also discover an entanglement gravity-like contributions and massive gravity at very small scales. This is remarkable considering that no Hilbert Einstein action, or variations expressing area invariance, were introduced. Our model also explains why semi classical approaches can work till way smaller scale than usually expected and present a new view on an Ultimate Unification of all forces, at very small scales.We also explore opportunities for falsifiability and validation of our model, as well as ideas for futuristic applications that may be worth considering, if U_{MF} was a suitable model for our universe U_{real}.

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Section: A Case For a Discrete Spacetime In U M F ?mentioning

confidence: 99%

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Maes¹

2020

Preprint

217

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“…There have been extensive and long-lasting discussions on the choice of stochastic calculus [5][6][7][8][9][10], relation between deterministic and stochastic description [11][12][13], as well as the covariance of theory under nonlinear transform of variables (NTV) [15][16][17][18]. Another related issue is discretization scheme for its path integral representation [19][20][21][22][23][24][25][26]. To date, nonlinear Langevin theory with multiplicative noises has not yet been properly understood.…”

Section: Introductionmentioning

confidence: 99%

Covariant formulation of nonlinear Langevin theory with multiplicative Gaussian white noises

Ding

Xing

2020

Phys. Rev. Research

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The multidimensional nonlinear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to nonlinear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.

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“…| is the functional Jacobian of the change of variables from η to h. We emphasize that even if the Langevin equation ( 1) is additive and does not depend on its time discretization, the expressions of the Jacobian and of the path-integral action do depend on the discretization chosen to write them [52][53][54]. We adopt the Stratonovich convention, which allows one to use the rules of calculus in the path integral [55] and to reverse time without changing the discretization [56,57]. Following Janssen [41], one then linearizes the square in the exponent of (5) using a "response field" ĥi (t ) to obtain the MSRJD action.…”

Section: Brst Susymentioning

confidence: 99%

Supersymmetries in nonequilibrium Langevin dynamics

et al. 2021

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Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that contrary to common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise-provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in nonequilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

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Building a path-integral calculus: a covariant discretization approach

Cited by 29 publications

References 74 publications

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Covariant formulation of nonlinear Langevin theory with multiplicative Gaussian white noises

Supersymmetries in nonequilibrium Langevin dynamics

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