61 research outputs found
How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
Several years ago we demonstrated that the Casimir energy for perfectly
reflecting and imperfectly reflecting parallel plates gravitated normally, that
is, obeyed the equivalence principle. At that time the divergences in the
theory were treated only formally, without proper regularization, and the
coupling to gravity was limited to the canonical energy-momentum-stress tensor.
Here we strengthen the result by removing both of those limitations. We
consider, as a toy model, massless scalar fields interacting with
semitransparent (-function) potentials defining parallel plates, which
become Dirichlet plates for strong coupling. We insert space and time
point-split regulation parameters, and obtain well-defined contributions to the
self- energy of each plate, and the interaction energy between the plates.
(This self-energy does not vanish even in the conformally-coupled,
strong-coupled limit.) We also compute the local energy density, which requires
regularization near the plates. In general, the energy density includes a
surface energy that resides precisely on the boundaries. This energy is also
regulated. The gravitational interaction of this well-defined system is then
investigated, and it is verified that the equivalence principle is satisfied.Comment: 14 pages, 4 figure
Three-body Casimir-Polder interactions
As part of our program to develop the description of three-body effects in
quantum vacuum phenomena, we study the three-body interaction of two
anisotropically polarizable atoms with a perfect electrically conducting plate,
a generalization of earlier work. Three- and four-scattering effects are
important, and lead to nonmonotonic behavior.Comment: 10 pages, 5 figures, for the proceedings of the conference
Mathematical Structures in Quantum Systems, Benasque, Spain, July 2012, to be
published in Nuovo Ciment
A Unified Treatment of the Characters of SU(2) and SU(1,1)
The character problems of SU(2) and SU(1,1) are reexamined from the
standpoint of a physicist by employing the Hilbert space method which is shown
to yield a completely unified treatment for SU(2) and the discrete series of
representations of SU(1,1). For both the groups the problem is reduced to the
evaluation of an integral which is invariant under rotation for SU(2) and
Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by
applying a rotation to a unit position vector in SU(2) and a Lorentz
transformation to a unit SO(2,1) vector which is time-like for the elliptic
elements and space-like for the hyperbolic elements in SU(1,1). The details of
the procedure for the principal series of representations of SU(1,1) differ
substantially from those of the discrete series.Comment: 31 pages, RevTeX, typos corrected. To be published in Journal of
Mathematical Physic
Many-Body Contributions to Green's Functions and Casimir Energies
The multiple scattering formalism is used to extract irreducible N-body parts
of Green's functions and Casimir energies describing the interaction of N
objects that are not necessarily mutually disjoint. The irreducible N-body
scattering matrix is expressed in terms of single-body transition matrices. The
irreducible N-body Casimir energy is the trace of the corresponding irreducible
N-body part of the Green's function. This formalism requires the solution of a
set of linear integral equations. The irreducible three-body Green's function
and the corresponding Casimir energy of a massless scalar field interacting
with potentials are obtained and evaluated for three parallel semitransparent
plates. When Dirichlet boundary conditions are imposed on a plate the Green's
function and Casimir energy decouple into contributions from two disjoint
regions. We also consider weakly interacting triangular--and parabolic-wedges
placed atop a Dirichlet plate. The irreducible three-body Casimir energy of a
triangular--and parabolic-wedge is minimal when the shorter side of the wedge
is perpendicular to the Dirichlet plate. The irreducible three-body
contribution to the vacuum energy is finite and positive in all the cases
studied.Comment: 22 pages, 8 figure
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