Vacuum polarization and classical self-action near higher-dimensional defectsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 5 июня 2017 г.
Аннотация:We analyze the gravity-induced effects associated with a massless
scalar field in a higher-dimensional spacetime being the tensor
product of (d-n)-dimensional Minkowski space and n-dimensional
spherically/cylindrically-symmetric space with a solid/planar
angle deficit. These spacetimes are considered as simple models
for a multidimensional global monopole (if $n\geqslant 3$)
or cosmic string (if $n=2$) with (d-n-1) flat extra
dimensions. Thus, we refer to them as conical backgrounds. In
terms of the angular deficit value, we derive the perturbative
expression for the scalar Green's function, valid for any
$d\geqslant 3$ and $2\leqslant n\leqslant d-1$, and
compute it to the leading order. With the use of this Green's
function we compute the renormalized vacuum expectation value of
the field square ${\langle \phi^{2}(x)\rangle}_{ren}$ and the
renormalized vacuum averaged of the scalar-field's energy-momentum
tensor ${\langle T_{MN}(x)\rangle}_{ren}$ for arbitrary d and
n from the interval mentioned above and arbitrary coupling
constant to the curvature.
In particular, we revisit the computation of the
vacuum polarization effects for a non-minimally coupled massless
scalar field in the spacetime of a straight cosmic string.
The same Green's function enables to consider the old purely
classical problem of the gravity-induced self-action of a
classical pointlike scalar or electric charge, placed at rest at some
fixed point of the space under consideration.
To deal with divergences, which appear in consideration of the
both problems, we apply the dimensional-regularization technique,
widely used in quantum field theory. The explicit dependence
of the results upon the dimensionalities of both the bulk and
conical submanifold, is discussed.