文档介绍：Semiclassical Effects Induced by
Aharonov-Bohm Interaction Between a
Cosmic String and a Scalar Field
M. E. X. Guimar˜aes
Department of Physics and Astronomy
University of Wales, College of Cardiff
PO Box 913, Cardiff CF2 3YB, UK
14 February 1997
Abstract
In the context of the vacuum polarization effect, we consider the
backreaction of the energy-momentum tensor of a charged scalar field
on the background metric of a cosmic string carrying a ic flux
1
Φ. Working within the semiclassical approach to the Einstein eqs. we
find the first-order (inh ¯) metric associated to the ic flux cos-
mic string. We show that the contribution to the vacuum polarization
ing from the Aharonov-Bohm interaction is larger than the
ing from the non-trivial gravitational interaction.
Classification PACS: 81T20, 83C47
Keywords: Cosmic Strings, Vacuum Polarization, Aharonov-Bohm in-
teraction
Introduction
In General Relativity, a static, straight axially symmetric cosmic string is
described by the metric [1]
ds2 = −dt2 + dz2 + dρ2 + B2ρ2dϕ2 (1)
in cylindrical coordinates (t, z, ρ, ϕ) such that ρ≥ 0and0≤ϕ<
constant B is related to the linear mass density µ of the string1: B =1−4µ.
For GUT strings, µ is of order µ ∼ 1022 g/cm.
1Throughout this paper, we work in the system of units in which G = c =1and
¯h∼ × 10−66 cm2.
2
Metric (1) is locally but not globally flat. The presence of the string leads
to an azymuthal deficit angle ∆= 8πµ and, as a result, this spacetime has a
conical singularity [2]. One of the most interesting features of this spacetime
is that fields and particles are sensitive to its global structure and physical
effects may arise due solely to the global properties of this metric. One of
these effects - the um polarization - has been extensively studied in the
literature [3, 4] and can be understood as an analog to the Casimir effect [5] in
which the conducting planes here form an angle equal to the deficit angle ∆.
Then, a sc