Remarks on Weyl geometry and quantum mechanics

Carroll, Robert

doi:10.48550/arxiv.0705.3921

Cited by 7 publications

(11 citation statements)

References 35 publications

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“…The Ricci flow has provided many far-reaching insights into long-standing problems in topology and geometry [1,2]. Recent works [8,9,10,11,12,13,14,15] have shed light on applications of conformal symmetry and the Ricci flow to foundational issues in quantum mechanics. In this contribution we have established a 1-to-1 correspondence between conformally flat metrics on configuration space, and quantum mechanics on that same space.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

On the Ricci flow and emergent quantum mechanics

Isidro

Santander

Córdoba

2009

J. Phys.: Conf. Ser.

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The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential function that is proportional to the Ricci scalar curvature of configuration space. This allows one to obtain Schroedinger quantum mechanics from Perelman's action functional: the quantum-mechanical wavefunction is the exponential of i times the conformal factor of the metric on configuration space. We explore links with the recently discussed emergent quantum mechanics.

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Section: Discussion and Perspectivesmentioning

confidence: 99%

On the Ricci flow and emergent quantum mechanics

Isidro

Santander

Córdoba

2009

J. Phys.: Conf. Ser.

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“…We follow mainly the presentation by Folland [36], where a modern treatment of Weyl geometry is developed. Other presentations of Weyl geometry appear in [26,29,30,33] and references therein.…”

Section: Weyl Geometrymentioning

confidence: 99%

“…Integrable versions of Dirac's theory were also proposed [28,29]. A recent review on the applications of Weyl geometry to gravitation and quantum mechanics is presented in [30].…”

Section: Introductionmentioning

confidence: 99%

Thin-disk models in an integrable Weyl–Dirac theory

Vieira

Letelier

2014

Gen Relativ Gravit

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We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in the Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303Phys. 29, (1999. The main differences between these solutions and the corresponding general relativistic one are analyzed, focusing on the behavior of physical observables (rotation curves of test particles, density and pressure profiles). We consider the case in which test particles move on Weyl geodesics. The same rotation curve can be obtained from many different solutions of the Weyl-Dirac theory, although some of these solutions present strong qualitative differences with respect to the usual general relativistic model (such as the appearance of a ring-like density profile). In particular, for typical galactic parameters all rotation curves of the Weyl-Dirac model present Keplerian fall-off. As a consequence, we conclude that a more thorough analysis of the problem requires the determination of the gauge function β on galactic scales, as well as restrictions on the test-particle behavior under the action of the additional geometrical fields introduced by this theory.

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“…[3,18,19,20]; the role of conformal symmetry and Ricci flow has been extensively studied in refs. [4,5,6,7]; the closely related emergent quantum mechanics has been dealt with in refs. [22,23,11,12].…”

Section: Proof Of the Corollarymentioning

confidence: 99%

“…Perhaps more surprising is the fact that it also has interesting applications in physics, where two important occurrences are conformal gravity [25], and the low-energy effective action of string theory [9]. Recent works [5,6,7,8] have shed light on applications of the Ricci flow to foundational issues in quantum mechanics. The present contribution is a continuation of previous research [1,14,15,16] on the exciting interrelation between Ricci flow, quantum mechanics and gravity.…”

Section: Introductionmentioning

confidence: 99%