Remarks on some quantum effects in the spacetime of a cosmic string (original) (raw)
Quantum vacuum interaction between two cosmic strings revisited
Physical Review D, 2014
We reconsider the quantum vacuum interaction energy between two straight parallel cosmic strings. This problem was discussed several times in an approach treating both strings perturbatively and treating only one perturbatively. Here we point out that a simplifying assumption made in [1] can be justified and show that, despite the global character of the background, the perturbative approach delivers a correct result. We consider the applicability of the scattering methods, developed in the past decade for the Casimir effect, for the cosmic string and find it not applicable. We calculate the scattering T-operator on one string. Finally, we consider the vacuum interaction of two strings when each carries a two dimensional delta function potential.
In this paper we analyze the relativistic quantum motion of charged spin-0 and spin-1 2 particles in the presence of a uniform magnetic field and scalar potentials in the cosmic string spacetime. In order to develop this analysis, we assume that the magnetic field is parallel to the string and the scalar potentials present a cylindrical symmetry with their center on the string. Two distinct configurations for the scalar potential, S(r), are considered: (i) the potential proportional to the inverse of the polar distance, i.e., S ∝ 1/r, and (ii) the potential proportional to this distance, i.e., S ∝ r. The energy spectra are explicitly computed for different physical situations and their dependences on the magnetic field strength and scalar coupling constants are presented.
Cosmic Rays as Elementary Strings in Quantum Relativity
The elementary Cosmic Ray Spectrum derives from the transformation of the Planck-String-Boson at the birth of the universe. The following tabulation relates those transformation in energy and the modular duality between the distance parameters of the macrocosm of classical spacetime geometry and the microcosm of the quantum realm.
On some classical and quantum effects due to gravitational fields
Brazilian Journal of Physics, 2006
We consider the gravitational fields generated by a cosmic string, a global monopole and a tubular matter with interior magnetic field (Safko-Witten space-time), and examine some classical and quantum effects due to these fields. We investigate the Aharonov-Bohm effect in the space-time of a cosmic string, using the loop variables. In the space-time of a global monopole, we calculate the total energy radiated by a uniformly moving charged scalar particle, for small solid angle deficit. We show that the radiated energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. In the Safko-Witten space-time, we investigate the existence of an electrostatic self-force on a charged particle. We also consider a hydrogen atom in the background space-time generated by a cosmic string and we find the solutions of the corresponding Dirac equation and we determine the energy levels of the atom. We investigate how the topological features of this space-time lead to shifts in the energy levels as compared with the flat Minkowski space-time. We study the behavior of non-relativistic quantum particles interacting with a Kratzer potential in the space-time generated by a global monopole and we find the energy spectrum in the presence of this topological defect. In the Safko-Witten space-time, an investigation is also made concerning the interaction of an harmonic oscillator with this background gravitational field.
Gravitational effect of the quantum vacuum outside a cosmic string
Classical and Quantum Gravity, 1992
The conical geometry of a static cylindrical!}' symmetric cosmic string, causes a non-vanishing contribution to the vacuum expectation value of the energymomentum tensor of a quantum field. Here we construct a model of a cosmic string taking into account the gravi tational field of this energy-density. The .«trongly curved interior of the siring is modelled by a homogeneous fluid with vanishing tangential and radial stress. The integrated effect of vacuum polarisation in this region is assumed to be accounted for by a singular layer with a traceless energy-momentum surface density at the surface of the string. The total Tolman mass of the system is positive, so the string produces an attractive gravitational field.
Topics in String Theory and Quantum Gravity 1
This Paper Focus about several connections between. String Theory and some of its implications with Gravity highligting how are necessary approximations to involve Quantum Gravity.
International Journal of Geometric Methods in Modern Physics
From a study of an oscillator in a 4D noncommutative (NC) spacetime, we establish the Hamilton equations of motion. The formers are solved to give the oscillator position and momentum coordinates. These coordinates are used to build a metric similar to that describing a cosmic string. On this basis, Dirac and Klein–Gordon oscillators are investigated. Their spectrum and dynamics are analyzed giving rise to novel interesting properties.
The Effect of Spatial Curvature on Classical and Quantum Strings
International Journal of Modern Physics, 1996
We study the effects of the spatial curvature on the classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson-Walker spacetimes with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the spacetime: the selfconsistent solution to the Einstein equations is a spatially closed (K > 0) spacetime with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K ≤ 0 exist. We semi-classically quantize the circular strings and find the mass m in each case. For K > 0, the very massive strings, oscillating on the full hypersphere, have m 2 ∼ Kn 2 (n ∈ N 0 ) independent of α ′ and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m 2 α ′ ∼ n and a finite number of states N ∼ 1/(Kα ′ ). For K < 0, there are infinitely many string states with masses m log m ∼ n, that is, the level spacing grows slower than n. The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.
String Theory in Cosmological Spacetimes
String Theory in Curved Space Times, 1998
Progress on string theory in curved spacetimes since 1992 are reviewed. After a short introduction on strings in Minkowski and curved spacetimes, we focus on strings in cosmological spacetimes. The classical behaviour of strings in FRW and inationary spacetimes is now understood in a large extent from various types of explicit string solutions. Three dierent t ypes of behaviour appear in cosmological spacetimes: unstable, dual to unstable and stable. F or the unstable strings, the energy and size grow for large scale factors R 1 , proportional to R. F or the dual to unstable strings, the energy and size blow up for R 0 a s 1 =R. F or stable strings, the energy and proper size are bounded. (In Minkowski spacetime, all string solutions are of the stable type). Recent progress on self-consistent solutions to the Einstein equations for string dominated universes is reviewed. The energy-momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is determined. The selfconsistent string solution exhibits the realistic matter dominated behaviour R (X 0 ) 2=3 for large times and the radiation dominated behaviour R (X 0 ) 1=2 for early times. Finally, w e report on the exact integrability of the string equations plus the constraints in de Sitter spacetime that allows to systematically nd exact string solutions by soliton methods and the multistring solutions. Multistring solutions are a new feature in curved spacetimes. That is, a single worldsheet simultaneously describes many dierent and independent strings. This phenomenon has no analogue in at spacetime and appears as a consequence of the coupling of the strings with the spacetime geometry.
Landau quantization in the spinning cosmic string spacetime
Annals of Physics, 2014
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having finite width and uniformly filled with both material and vacuum energies.
Geometric quantum phases from Lorentz symmetry breaking effects in the cosmic string spacetime
Physical Review D, 2014
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is investigated. It is shown that the Dirac equation can be written in terms of an effective metric and a relativistic geometric phase stems from the topology of the cosmic string spacetime and the Lorentz symmetry breaking effects. Further, the nonrelativistic limit of the Dirac equation is discussed and it is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-1/2 particle.
Strings and multi-strings in black hole and cosmological spacetimes
Arxiv preprint hep-th/9504007, 1995
Recent results on classical and quantum strings in a variety of black hole and cosmological spacetimes, in various dimensions, are presented. The curved backgrounds under consideration include the 2 + 1 black hole anti de Sitter spacetime and its dual, the black string, the ordinary D ≥ 4 black holes with or without a cosmological constant, the de Sitter and anti de Sitter spacetimes and static Robertson-Walker spacetimes. Exact solutions to the string equations of motion and constraints, representing circular strings, stationary open strings and dynamical straight strings, are obtained in these backgrounds and their physical properties (length, energy, pressure) are described. The existence of multi-string solutions, describing finitely or infinitely many strings, is shown to be a general feature of spacetimes with a positive or negative cosmological constant. Generic approximative solutions are obtained using the string perturbation series approach, and the question of the stability of the solutions is addressed. Furthermore, using a canonical quantization procedure, we find the string mass spectrum in de Sitter and anti de Sitter spacetimes. New features as compared to the string spectrum in flat Minkowski spacetime appear, for instance the fine-structure effect at all levels beyond the graviton in both de Sitter and anti de Sitter spacetimes, and the non-existence of a Hagedorn temperature in anti de Sitter spacetime. We discuss the physical implications of these results. Finally, we consider the effect of spatial curvature on the string dynamics in Robertson-Walker spacetimes.
arXiv (Cornell University), 2023
We study the relativistic quantum motion of a spineless particle using the Feshbach-Villars (FV) formalism in the spinning cosmic string spacetime. The movement equations are derived using the first-order FV formulation of the Klein-Gordon (KG) equation. We apply the equation of motion (a) to study the motion of the particle confined to a rigid-wall potential, (b) motion in the presence of a Coulomb-type potential, and (c) particle interacting with the Feshbach-Villars oscillator (FVO). The energy levels and wave functions are obtained for the three cases. Our study focused on the impact of rotation and curvature on the energy levels of the particle.
Covariant relativistic spacetime string
A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg (1941) [1], and further developed by Horwitz and Piron (1973) [2]. We describe the spacetime string using the solutions of relativistic harmonic oscillator [3]. The mass and energy spectrum are derived. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the description of a quantized string. Some comparison is made with known string models.
Cosmic Strings and Quintessence
Chinese Physics Letters, 2003
We present a new Lorentz gauge invariant U (1) topological field theory in Riemann-Cartan spacetime manifold U 4. By virtue of the decomposition theory of U (1) gauge potential and the φ-mapping topological current theory, it is proved that the U (1) complex scalar field φ(x) can be looked upon as the order parameter field in our Universe, and the set of zero points of φ(x) create the cosmic strings as the spacetime defects in the early Universe. In the standard cosmology this complex scalar order parameter field possesses negative pressure, provides an accelerating expansion of Universe and be able to explain the inflation in the early Universe. Therefore this complex scalar field is not only the order parameter field created the cosmic strings, but also reasonably behaves as the quintessence, the dark energy.
International Journal of Modern Physics A, 2016
The behavior of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string space–time is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor [Formula: see text]. Then, by introducing a scalar potential as a modification of the mass term of the Klein–Gordon equation, it is shown that the Klein–Gordon equation in the cosmic string space–time is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein–Gordon equation can be obtained.
Equivalence of String Classical and Quantum Energy
Scientific Research Publishing, 2020
Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single are orated waves. Each wave consists of n photons or quant
Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single are orated waves. Each wave consists of n pho-tons or quanta.
Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space–time
General Relativity and Gravitation, 2019
We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.
In this paper, we investigate the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor, associated with a massive fermionic field, induced by the presence of a cosmic string in the anti-de Sitter (AdS) spacetime. In order to develop this analysis we construct the complete set of normalized eigenfunctions in the corresponding spacetime. We consider a special case of boundary conditions on the AdS boundary, when the MIT bag boundary condition is imposed on the field operator at a finite distance from the boundary, which is then taken to zero. The FC and the VEV of the energy-momentum tensor are decomposed into the pure AdS and stringinduced parts. Because the analysis of one-loop quantum effects in the AdS spacetime has been developed in the literature, here we are mainly interested to investigate the influence of the cosmic string on the VEVs. The string-induced part in the VEV of the energy-momentum tensor is diagonal and the axial and radial stresses are equal to the energy density. For points near the string, the effects of the curvature are subdominant and to leading order, the VEVs coincide with the corresponding VEVs for the cosmic string in the Minkowski bulk. At large proper distances from the string, the decay of the VEVs show a power-law dependence of the distance for both massless and massive fields. This is in contrast to the case of the Minkowski bulk where, for a massive field, the string-induced parts decay exponentially.