7,676 research outputs found
Non-Gaussian wave functionals in Coulomb gauge Yang--Mills theory
A general method to treat non-Gaussian vacuum wave functionals in the
Hamiltonian formulation of a quantum field theory is presented. By means of
Dyson--Schwinger techniques, the static Green functions are expressed in terms
of the kernels arising in the Taylor expansion of the exponent of the vacuum
wave functional. These kernels are then determined by minimizing the vacuum
expectation value of the Hamiltonian. The method is applied to Yang--Mills
theory in Coulomb gauge, using a vacuum wave functional whose exponent contains
up to quartic terms in the gauge field. An estimate of the cubic and quartic
interaction kernels is given using as input the gluon and ghost propagators
found with a Gaussian wave functional.Comment: 27 pages, 21 figure
Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional
black hole solution of the Einstein's field equations with a negative
cosmological constant. First, we analyze the space of classical solutions in a
mode decomposition and we characterize the collection of all admissible
boundary conditions of Robin type which can be imposed at infinity. Secondly,
we investigate whether, for a given boundary condition, there exists a ground
state by constructing explicitly its two-point function. We demonstrate that
for a subclass of the boundary conditions it is possible to construct a ground
state that locally satisfies the Hadamard property. In all other cases, we show
that bound state mode solutions exist and, therefore, such construction is not
possible.Comment: 17 pages, 3 figure
Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type
We study a real, massive Klein-Gordon field in the Poincar\'e fundamental
domain of the -dimensional anti-de Sitter (AdS) spacetime, subject to a
particular choice of dynamical boundary conditions of generalized Wentzell
type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon
equation, with the source term fixed by the normal derivative of the scalar
field at the boundary. This naturally defines a field in the conformal boundary
of the Poincar\'e fundamental domain of AdS. We completely solve the equations
for the bulk and boundary fields and investigate the existence of bound state
solutions, motivated by the analogous problem with Robin boundary conditions,
which are recovered as a limiting case. Finally, we argue that both Robin and
generalized Wentzell boundary conditions are distinguished in the sense that
they are invariant under the action of the isometry group of the AdS conformal
boundary, a condition which ensures in addition that the total flux of energy
across the boundary vanishes.Comment: 12 pages, 1 figure. In V3: refs. added, introduction and conclusions
expande
Quantum field theory on rotating black hole spacetimes
This thesis is concerned with the development of a general method to compute
renormalised local observables for quantum matter fields, in a given quantum
state, on a rotating black hole spacetime. The rotating black hole may be
surrounded by a Dirichlet mirror, if necessary, such that a regular,
isometry-invariant vacuum state can be defined. We focus on the case of a
massive scalar field on a (2+1)-dimensional rotating black hole, but the method
can be extended to other types of matter fields and higher-dimensional rotating
black holes.
The Feynman propagator of the matter field in the regular, isometry-invariant
state is written as a sum over mode solutions on the complex Riemannian section
of the black hole. A Hadamard renormalisation procedure is implemented at the
level of the Feynman propagator by expressing its singular part as a sum over
mode solutions on the complex Riemannian section of rotating Minkowski
spacetime. This allows us to explicitly renormalise local observables such as
the vacuum polarisation of the quantum field.
The method is applied to the vacuum polarisation of a real massive scalar
field on a (2+1)-dimensional warped AdS3 black hole surrounded by a mirror.
Selected numerical results are presented, demonstrating the numerical efficacy
of the method. The existence of classical superradiance and the classical
linear mode stability of the warped AdS3 black hole to massive scalar field
perturbations are also analysed.Comment: PhD thesis submitted to the University of Nottingha
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