Path Integral Quantization of the Sphere

Reartes, Walter

doi:10.1007/978-1-4419-9058-7_14

Cited by 2 publications

(4 citation statements)

References 8 publications

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“…The same reasoning is true for non-relativistic and relativistic particles and computing the Path Integrals with Euclidean or Minkowski metrics [77,112,113]. Indeed, the apparition of a potential also appears in Klein Gordon (field) equation for Boson in a curved space (see chapter 5 in [345]) and in Dirac's equations for Fermions (see equation 5.23 in [345] is also always satisfied by spinors when taking the second order version of Dirac's equation which is of the form of Klein Gordon equation).…”

Section: Let Us Note the Analysismentioning

confidence: 85%

“…As computed in [77,112], the effect amounts to introduce an that it will happen at this stage of the reasoning. However as the folds live outside the background spacetime of U M F , by construction.…”

Section: Let Us Note the Analysismentioning

confidence: 99%

“…What is interesting is that, at quantum scales, gravity is the result of preventing supra luminous propagators, entangled virtual particles emitted near a source of energy or particle and EPR entanglement. It is derived from quantum physics and it is not just a perturbative result or a macroscopic or statistical result as are QFT as well as GR 112 This derivation results solely from the rules (folds and nothing supra luminous) of UMF . It is not the result of a priori using, adapting or extending Hilbert-Einstein action as is done in (QFT gravity, superstrings and theories like LQG (the whole family of variations as for examples reviewed in [243] 113 ) that 112 Later, we will also derive GR from Statistical Physics / Thermodynamics considerations of our model.…”

Section: Gravity Emergence From Entanglement and No Supra Luminositymentioning

confidence: 99%

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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: Let Us Note the Analysismentioning

confidence: 85%

Section: Let Us Note the Analysismentioning

confidence: 99%

Section: Gravity Emergence From Entanglement and No Supra Luminositymentioning

confidence: 99%

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Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Maes¹

2020

Preprint

217

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“…Then, a Green function is finally obtained which coincides with that resulting from the infinitesimal propagator proposed in [25]. In the construction of this propagator, the integration is performed in the tangent space of S 1 .…”

Section: Introductionmentioning

confidence: 92%

Holomorphic Path Integrals in Tangent Space for Flat Manifolds

Capobianco¹,

Reartes²

2017

Preprint

Self Cite

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In this paper we study the quantum evolution in a flat Riemannian manifold. The holomorphic functions are defined on the cotangent bundle of this manifold. We construct Hilbert spaces of holomorphic functions in which the scalar product is defined using the exponential map. The quantum evolution is proposed by means of an infinitesimal propagator and the holomorphic Feynman integral is developed via the exponential map. The integration corresponding to each step of the Feynman integral is performed in the tangent space. Moreover, in the case of S 1 , the method proposed in this paper naturally takes into account paths that must be included in the development of the corresponding Feynman integral.

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Path Integral Quantization of the Sphere

Cited by 2 publications

References 8 publications

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

Holomorphic Path Integrals in Tangent Space for Flat Manifolds

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