28 research outputs found
Coherent states for the hydrogen atom: discrete and continuous spectra
We construct the systems of generalised coherent states for the discrete and
continuous spectra of the hydrogen atom. These systems are expressed in
elementary functions and are invariant under the (discrete spectrum)
and (continuous spectrum) subgroups of the dynamical symmetry group
of the hydrogen atom. Both systems of coherent states are particular
cases of the kernel of integral operator which interwines irreducible
representations of the group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.
Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
The mathematical formalism necessary for the diagramatic evaluation of
quantum corrections to a conformally invariant field theory for a
self-interacting scalar field on a curved manifold with boundary is considered.
The evaluation of quantum corrections to the effective action past one-loop
necessitates diagramatic techniques. Diagramatic evaluations and higher
loop-order renormalisation can be best accomplished on a Riemannian manifold of
constant curvature accommodating a boundary of constant extrinsic curvature. In
such a context the stated evaluations can be accomplished through a consistent
interpretation of the Feynman rules within the spherical formulation of the
theory for which the method of images allows. To this effect, the mathematical
consequences of such an interpretation are analyzed and the spherical
formulation of the Feynman rules on the bounded manifold is, as a result,
developed.Comment: 12 pages, references added. To appear in Classical and Quantum
Gravit
"Peeling property" for linearized gravity in null coordinates
A complete description of the linearized gravitational field on a flat
background is given in terms of gauge-independent quasilocal quantities. This
is an extension of the results from gr-qc/9801068. Asymptotic spherical
quasilocal parameterization of the Weyl field and its relation with Einstein
equations is presented. The field equations are equivalent to the wave
equation. A generalization for Schwarzschild background is developed and the
axial part of gravitational field is fully analyzed. In the case of axial
degree of freedom for linearized gravitational field the corresponding
generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally,
the asymptotics at null infinity is investigated and strong peeling property
for axial waves is proved.Comment: 27 page
Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary
The effects of quantum corrections to a conformally invariant scalar field
theory on a curved manifold of positive constant curvature with boundary are
considered in the context of a renormalisation procedure. The renormalisation
of the theory to second order in the scalar self-coupling pursued herein
involves explicit calculations of up to third loop-order and reveals that, in
addition to the renormalisation of the scalar self-coupling and scalar field,
the removal of all divergences necessitates the introduction of conformally
non-invariant counterterms proportional to and in the
bare scalar action as well as counterterms proportional to , and
in the gravitational action. The substantial backreaction effects and
their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the
cut-off and in p.4 regarding the gravitational action. Certain
reference-related ommission corrected. To appear in Classical and Quantum
Gravit
Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7
The BPS equations in M-theory for solutions with 16 residual supersymmetries,
symmetry, and asymptotics,
were reduced in [arXiv:0806.0605] to a linear first order partial differential
equation on a Riemann surface with boundary, subject to a non-trivial quadratic
constraint. In the present paper, suitable regularity and boundary conditions
are imposed for the existence of global solutions. We seek regular solutions
with multiple distinct asymptotic regions, but find that,
remarkably, such solutions invariably reduce to multiple covers of the M-Janus
solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the
half-BPS M-Janus solution. In particular, we prove analytically that no other
smooth deformations away from the M-Janus solution exist, as such deformations
invariably violate the quadratic constraint. These rigidity results are
contrasted to the existence of half-BPS solutions with non-trivial 4-form
fluxes and charges asymptotic to . The results are related to
the possibility of M2-branes to end on M5-branes, but the impossibility of
M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions
with simultaneous and asymptotic regions.Comment: 52 pages, 2 figures, pdf-latex. Minor change
Study of a Class of Four Dimensional Nonsingular Cosmological Bounces
We study a novel class of nonsingular time-symmetric cosmological bounces. In
this class of four dimensional models the bounce is induced by a perfect fluid
with a negative energy density. Metric perturbations are solved in an analytic
way all through the bounce. The conditions for generating a scale invariant
spectrum of tensor and scalar metric perturbations are discussed.Comment: 16 pages, 10 figure
Perturbative Evaluation of the Zero-Point function for Self-Interacting Scalar Field on a Manifold with Boundary
The character of quantum corrections to the gravitational action of a
conformally invariant field theory for a self-interacting scalar field on a
manifold with boundary is considered at third loop-order in the perturbative
expansion of the zero-point function. Diagramatic evaluations and higher
loop-order renormalisation can be best accomplished on a Riemannian manifold of
constant curvature accommodating a boundary of constant extrinsic curvature.
The associated spherical formulation for diagramatic evaluations reveals a
non-trivial effect which the topology of the manifold has on the vacuum
processes and which ultimately dissociates the dynamical behaviour of the
quantised field from its behaviour in the absence of a boundary. The first
surface divergence is evaluated and the necessity for simultaneous
renormalisation of volume and surface divergences is shown.Comment: 19 pages, 2 figures, one figure and references added, substantial
extension of the discussion. To appear in Classical and Quantum Gravit
Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters
are reduced to two functions with fixed values of parameters, which differ from
the original ones by integers. It is shown that in the case of integer and/or
half-integer values of parameters there are only three types of algebraically
independent Gauss hypergeometric functions. The epsilon-expansion of functions
of one of this type (type F in our classification) demands the introduction of
new functions related to generalizations of elliptic functions. For the five
other types of functions the higher-order epsilon-expansion up to functions of
weight 4 are constructed. The result of the expansion is expressible in terms
of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop
off-shell propagator diagrams with one massive line and q massless lines and
q-loop bubble with two-massive lines and q-1 massless lines are considered. The
code (Mathematica/FORM) is available via the www at this URL
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 19 pages, LaTeX, 1-eps figure; v5: The code (Mathematica/FORM) is
available via the www http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htm