Renormalized scalar propagator around a dispiration

Lorenci, V. A. De; Moreira, E. S.

doi:10.1103/physrevd.67.124002

Cited by 10 publications

(41 citation statements)

References 27 publications

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“…[37] used the terminology 'cosmic dislocation' to refer to this chiral cosmic string, we will follow the same terminology coined by the authors in Ref. [39] who called this combination as 'cosmic dispiration'. It seems more appropriate due to the singularity associated to the screw dislocation aspect of the defect.…”

Section: Introductionmentioning

confidence: 99%

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Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime

Mota

Mello

Bakke

2018

Int. J. Mod. Phys. D

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In this paper we present a complete and detailed analysis of the calculation of both the Wightman function and the vacuum expectation value of the energy-momentum tensor that arise from quantum vacuum fluctuations of massive and massless scalar fields in the cosmic dispiration spacetime, which is formed by the combination of two topological defects: a cosmic string and a screw dislocation. This spacetime is obtained in the framework of the Einstein-Cartan theory of gravity and is considered to be a chiral space-like cosmic string. For completeness we perform the calculation in a high-dimensional spacetime, with flat extra dimensions. We found closed expressions for the the energy-momentum tensor and, in particular, in (3+1)-dimensions, we compare our results with existing previous ones in the literature for the massless scalar field case.

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Section: Introductionmentioning

confidence: 99%

“…In particular, only a few studies about cosmic dispiration spacetime, in the framework of quantum vacuum fluctuations, have been reported in the literature [60,39,61]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime

Mota

Mello

Bakke

2018

Int. J. Mod. Phys. D

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“…(4) becomes singular. Vacuum fluctuations of a massless scalar field φ around a cosmic dislocation have recently been reported in the literature [12]. Equations (5) and (7) show that when κ ′ → 0 the corresponding vacuum fluctuations become those associated with an ordinary cosmic string (see, e.g., [13]).…”

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confidence: 99%

“…(14) by considering the expressions for T µ ν in Ref. [12]. For example, if φ is conformally coupled, it follows that (5)], since the latter would be traveling nearly at the speed of light (recall that v = S/κ).…”

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Spinning strings, cosmic dislocations, and chronology protection

Lorenci

Moreira

2004

Phys. Rev. D

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A massless scalar field is quantized in the background of a spinning string with cosmic dislocation. By increasing the spin density toward the dislocation parameter, a region containing closed timelike curves (CTCs) eventually forms around the defect. Correspondingly, the propagator tends to the ordinary cosmic string propagator, leading therefore to a mean-square field fluctuation, which remains well behaved throughout the process, unlike the vacuum expectation value of the energy-momentum tensor, which diverges due to a subtle mechanism. These results suggest that back reaction leads to the formation of a "horizon" that protects from the appearance of CTCs.PACS numbers: 04.62.+v, 04.20.Gz, 11.27.+d Investigations on quantum theory around spinning defects go back to the late 1980s with the study of quantum mechanics of relativistic particles on the spinning cone [1]. Such a background is the Kerr-like solution of the Einstein equations in three dimensions, whose line element is given by (throughout the text c = = 1, and the metric parameters are nonnegative)where S and α are the spin and the disclination parameter, respectively [2]. Clearly Minkowski spacetime corresponds to S = 0 and α = 1. Lifting the geometry in Eq.(1) to four dimensions, one obtains the gravitational background around a spinning cosmic string [3], for whichAn inspection of Eqs.(1) and (2) shows that the region for which r < S/α contains CTCs, resulting that when S = 0 the corresponding spacetimes are not globally hyperbolic. It is not clear if quantum theory makes sense in nonglobaly hyperbolic spacetimes [4]. In fact, quantum mechanics on the spinning cone has shown that S = 0 spoils unitarity [1]. In the context of the second quantization around spinning cosmic strings [5], a recent analysis has revealed that a nonvanishing spin density S leads to divergent vacuum fluctuations [6].In order to recover boost invariance along the symmetry axis, the authors in Ref. [7] have "amended" the geometry in Eq. (2) by postulating a cosmic dislocation, such thatwhose metric tensor fits as solution of the Einstein equations, as well as solution of the Einstein-Cartan equations [8,9]. When S > κ, the region for which r < √ S 2 − κ 2 /α contains CTCs. When S < κ though, the spacetime is globally hyperbolic.Vacuum fluctuations typically diverge on the Cauchy surface (chronology horizon), which separates a region with CTCs from another without CTCs (for a review see Ref. [10]). This fact has led to the chronology protection conjecture, according to which, physical laws do not allow the appearance of CTCs ("time machines") [11]. Although the geometry in Eq. (3) does not contain any Cauchy horizon [for S > κ, Eq. (3) describes an "eternal time machine"], it might be clarifying to study quantum effects in the corresponding spacetime as the metric parameters are adjusted such that CTCs are about to form. Using a massless scalar field as a probe, this work implements such an investigation by considering S < κ and by taking S → κ, i.e., arbitrarily close to t...

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“…In our case, the spins lie on an infinite cylinder of radius ρ o , with deficit angle 2π(1 − c) and screw dislocation k [12][13][14][15]. This 2-dimensional manifold is characterized by the line element written in cylindrical coordinates as…”

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Heisenberg spin textures on a cylinder with topological defects

Paula¹

2009

Braz. J. Phys.

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The present work aims to study equilibrium configurations of spins on a cylinder with topological defects such as screw dislocation and deficit angle. By making use of elliptic-f expansion method, which in turn utilizes the Jacobi elliptic functions, we obtain exact solutions of the nonlinear sigma model in this geometry. We have significant changes in the qualitative behavior of the solutions due to the presence of the parameter k of screw dislocation. In particular, the behavior of soliton-like solutions, characteristic of a cylinder without dislocation, was not found in the model here proposed. Keywords: Heisenberg's spins -nanomagnetism The nonlinear sigma model is the continuous limit of Heisenberg's hamiltonian for spins and has gained interest recently. It allows the study of equilibrium configurations of spins on non-trivial geometries such as cylinders, tori, ellipsoids, surfaces with negative curvature and so on [1][2][3][4]. The study of the stability of spin configurations and geometric frustration on different kinds of geometry are the two effects most explored with this model [5][6][7][8]. Defects such as punctures and impurities in the structure have also played an important role related to spin topological textures. In particular, we have introduced topological defects in an ideal cylinder such as screw dislocation. This defect is obtained by producing a longitudinal displacement in the structure, distorting the lattice helically. In this way we can study how the spin textures are modified in relation to the simple cylinder without these defects.Connections with fundamental areas and important technological applications can also be made: the "similarity" between the nonlinear sigma model in 2D and Yang-Mills in (3+1)D [9]; out-of-plane vortex (its core is similar to the central region of a soliton of spins). These out-of-plane vortex are important in several mechanisms of magnetic logic (MRAM), ultra-precise magnetic sensors, magnetic recording, etc. [10,11] The Heisenberg model takes into account only the interaction of each spin of the lattice with its first neighbors. By applying an external magnetic field, the Hamiltonian of the system is thenHere h ab is the 3 × 3 dimensionless interaction law matrix (metric of the internal space of spins), J is the exchange energy, and S a i denotes the a-th component of the spin of the i-th cell of the lattice, while < i, j > includes in the sum only the first neighbor cells j of each cell i. For isotropic interaction we have h ab = diag (1, 1, 1). The parameter g is the gyromagnetic factor of the spins in the material medium, µ is their magnetic momentum and B a is the a-th component of the external magnetic field. Eq. (1) is the hamiltonian for J > 0, describing the ferromagnetic case. In the antiferromagnetic case (J < 0), the spin vector S must be replaced by the Néel vector η = 1 2 ( S 1 − S 2 ), where the index distinguish two distinct sub-lattices in the more simple case.For sufficiently small distances between neighbor cells (and large spins) we...

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Renormalized scalar propagator around a dispiration

Cited by 10 publications

References 27 publications

Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime

Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime

Spinning strings, cosmic dislocations, and chronology protection

Heisenberg spin textures on a cylinder with topological defects

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