Classical and quantum aspects of particle propagation in external gravitational fields

Papini, G.

doi:10.1142/s0218271817501371

Cited by 8 publications

(9 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in agreement with the equation of geodesic deviation [17]. Notice that in (14) the vorticity is entirely due to R µναβ J αβ and that d 2 zµ ds 2 = 0 when the motion is irrotational.…”

Section: Vorticessupporting

confidence: 80%

“…Therefore, the potential K α is regular everywhere, which is physically desirable, but Φ G is singular. There may then be closed paths embracing the singularities along which the particle wave function must be made single-valued by means of appropriate quantization conditions [17]. It also follows from (10) that Fµν is a vortex along which the scalar particles are dragged with acceleration…”

Section: Vorticesmentioning

confidence: 99%

See 1 more Smart Citation

Structured objects in quantum gravity. The external field approximation

Papini

2018

Int. J. Mod. Phys. D

Self Cite

View full text Add to dashboard Cite

In the external field approximation (EFA) gravity and inertia are represented by a two-point vector that is the byproduct of symmetry breaking. The vector is accompanied by the appearance of classical, vortical structures. Its interaction range is, in general, that of the metric tensor, but, in the context of a simple symmetry breaking model, the range can be made finite by the presence of massive scalar particles. Vortices can then be produced that conceal matter making it effectively "dark". In EFA fermion relativistic vortices can be induced, in particular, by rotation. THE EXTERNAL FIELD APPROXIMATIONSymmetry breaking in quantum many-body systems gives rise to macroscopic objects like vortices in superconductors, dislocations in crystals and domain walls in ferromagnets. These structures normally appear in a quantum context, but behave classically. They are properties of matter, in the form other than particles, that emerge from a quantum background when quantum fluctuations become negligible. Here we consider the possibility that similar phenomena occur in quantum gravity, still far from the essential quantum regime that is supposed to take over at Planck's length. The suggestion comes from studies of covariant wave equations [1-5] that can be solved exactly to first order in the metric deviation γ µν = g µν − η µν , where η µν is the Minkowski metric and whose solutions are a useful tool in the study of the interaction of gravity with quantum systems [6][7][8][9][10][11][12].In the EFA context, gravity is represented exclusively by a two-point vector K λ (z, x) [13,14] that is known only if γ µν and its derivatives are known. In what follows the coordinates z µ refer to a frame that is moved by parallel displacement along a particle path and x µ to a particle local inertial frame. Though the essential steps of the discussion apply to any wave equation, spin is an unnecessary complication and is momentarily ignored. A brief discussion of fermions is given in section 4. Without loss of generality, we can therefore consider the Klein-Gordon equation that, in its minimal coupling form and after applying the Lanczos-DeDonder condition γ αν , ν −1/2γ σ σ , α = 0, becomes(1)We use unitsh = c = 1 and the notations are as in [12]. In particular, ∇ µ is the covariant derivative and partial derivatives with respect to a variable y µ are interchangeably indicated by ∂ µ , or by a comma followed by µ. The first order solution of (1) iswhereΦ G is the operatorΦwhere P is an arbitrary point, henceforth dropped, and φ 0 (x) is a wave packet solution of the free Klein-Gordon equationThe transformation (2) that makes the ground state of the system space-time dependent, results in a breakdown of symmetry. This is essentially produced by EFA because it is this approximation that generates the solution (2) and preserves its structure even at higher order iterations according to the relation φ(x) = Σ n φ (n) (x) = Σ n e −iΦG φ (n−1) . For simplicity we choose a plane wave for φ 0 . We also writeΦ G (x)φ 0 (x) ≡ Φ G (x)φ 0 (x) wh...

show abstract

Section: Vorticessupporting

confidence: 80%

Section: Vorticesmentioning

confidence: 99%

Structured objects in quantum gravity. The external field approximation

Papini

2018

Int. J. Mod. Phys. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…There may then be closed paths embracing the singularities along which the particle wave function must be made single-valued by means of appropriate quantization conditions [ 28 ]. It also follows from ( 75 ) that

is a vortex along which the scalar particles are dragged with acceleration

and relative acceleration

in agreement with the equation of geodesic deviation [ 28 ]. Notice that in ( 76 ) the vorticity is entirely due to

and that

when the motion is irrotational.…”

Section: Vorticesmentioning

confidence: 99%

“…The oscillations of

are similar to spin waves and obey the dispersion relation [ 28 , 31 ]

where s is the spin magnitude at a site,

is the spin-wave momentum and a is the lattice spacing. Upon quantization, spin waves give rise to quasiparticles that, by analogy with magnons, shall be called “gravons”.…”

Section: The One-dimensional Modelmentioning

confidence: 99%

Some Classical and Quantum Aspects of Gravitoelectromagnetism

Papini

2020

Entropy

Self Cite

View full text Add to dashboard Cite

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of “gravitoelectromagnetism” were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an XY-model.

show abstract

“…where R αβστ is the linearized Riemann tensor [25,26]. It follows from ( 8) that Φ G is not single-valued and that, after a gauge transformation, K α satisfies the equations…”

Section: Introductionmentioning

confidence: 99%

Condensation phenomena in gravity

Papini

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Gravity can play a role in critical phenomena. Topological singularities induce ground state degeneracy and break the continuum symmetry of the vacuum. They also generate momenta oscillations about an average momentum and a positive gravitational susceptibility. Gravitational analogues of the laws of Curie and Bloch have been found for a one-dimensional model. The critical temperature for a change in phase from unbound to isolated vortices has also been calculated in a XY -model.

show abstract

Classical and quantum aspects of particle propagation in external gravitational fields

Cited by 8 publications

References 50 publications

Structured objects in quantum gravity. The external field approximation

Structured objects in quantum gravity. The external field approximation

Some Classical and Quantum Aspects of Gravitoelectromagnetism

Condensation phenomena in gravity

Contact Info

Product

Resources

About