57 research outputs found
Solution to the ghost problem in fourth order derivative theories
We present a solution to the ghost problem in fourth order derivative
theories. In particular we study the Pais-Uhlenbeck fourth order oscillator
model, a model which serves as a prototype for theories which are based on
second plus fourth order derivative actions. Via a Dirac constraint method
quantization we construct the appropriate quantum-mechanical Hamiltonian and
Hilbert space for the system. We find that while the second-quantized Fock
space of the general Pais-Uhlenbeck model does indeed contain the negative norm
energy eigenstates which are characteristic of higher derivative theories, in
the limit in which we switch off the second order action, such ghost states are
found to move off shell, with the spectrum of asymptotic in and out S-matrix
states of the pure fourth order theory which results being found to be
completely devoid of states with either negative energy or negative norm. We
confirm these results by quantizing the Pais-Uhlenbeck theory via path
integration and by constructing the associated first-quantized wave mechanics,
and show that the disappearance of the would-be ghosts from the energy
eigenspectrum in the pure fourth order limit is required by a hidden symmetry
that the pure fourth order theory is unexpectedly found to possess. The
occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure
fourth order theories per se, but rather to be one which only arises when
fourth and second order theories are coupled to each other.Comment: 36 pages, revtex. Prepared for the proceedings of the 2006 Biennial
Meeting of the International Association for Relativistic Dynamics Version 2
contains an expanded discussion of the path integral quantization of the
Pais-Uhlenbeck fourth order oscillator theor
Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems
We present a solution to the cosmological constant, the zero-point energy,
and the quantum gravity problems within a single comprehensive framework. We
show that in quantum theories of gravity in which the zero-point energy density
of the gravitational field is well-defined, the cosmological constant and
zero-point energy problems solve each other by mutual cancellation between the
cosmological constant and the matter and gravitational field zero-point energy
densities. Because of this cancellation, regulation of the matter field
zero-point energy density is not needed, and thus does not cause any trace
anomaly to arise. We exhibit our results in two theories of gravity that are
well-defined quantum-mechanically. Both of these theories are locally conformal
invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based
quantum conformal gravity in four dimensions (a fourth-order derivative quantum
theory of the type that Bender and Mannheim have recently shown to be
ghost-free and unitary). Central to our approach is the requirement that any
and all departures of the geometry from Minkowski are to be brought about by
quantum mechanics alone. Consequently, there have to be no fundamental
classical fields, and all mass scales have to be generated by dynamical
condensates. In such a situation the trace of the matter field energy-momentum
tensor is zero, a constraint that obliges its cosmological constant and
zero-point contributions to cancel each other identically, no matter how large
they might be. Quantization of the gravitational field is caused by its
coupling to quantized matter fields, with the gravitational field not needing
any independent quantization of its own. With there being no a priori classical
curvature, one does not have to make it compatible with quantization.Comment: Final version, to appear in General Relativity and Gravitation (the
final publication is available at http://www.springerlink.com). 58 pages,
revtex4, some additions to text and some added reference
Limitations of the Standard Gravitational Perfect Fluid Paradigm
We show that the standard perfect fluid paradigm is not necessarily a valid
description of a curved space steady state gravitational source. Simply by
virtue of not being flat, curved space geometries have to possess intrinsic
length scales, and such length scales can affect the fluid structure. For modes
of wavelength of order or greater than such scales eikonalized geometrical
optics cannot apply and rays are not geodesic. Covariantizing thus entails not
only the replacing of flat space functions by covariant ones, but also the
introduction of intrinsic scales that were absent in flat space. In principle
it is thus unreliable to construct the curved space energy-momentum tensor as
the covariant generalization of a geodesic-based flat spacetime energy-momentum
tensor. By constructing the partition function as an incoherent average over a
complete set of modes of a scalar field propagating in a curved space
background, we show that for the specific case of a static, spherically
symmetric geometry, the steady state energy-momentum tensor that ensues will in
general be of the form
where the
anisotropic is a symmetric, traceless rank two tensor which
obeys . Such a type term is absent for an
incoherently averaged steady state fluid in a spacetime where there are no
intrinsic length scales, and in principle would thus be missed in a
covariantizing of a flat spacetime . While the significance of such
type terms would need to be evaluated on a case by case basis,
through the use of kinetic theory we reassuringly find that the effect of such
type terms is small for weak gravity stars where perfect fluid
sources are commonly used.Comment: Final version to appear in General Relativity and Gravitation (the
final publication is available at http://www.springerlink.com). 29 pages, 1
figur
Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole
Firstly we derive peculiar spherical Weyl solutions, using a general
spherically symmetric metric due to a massive charged object with definite mass
and radius. Afterwards, we present new analytical solutions for relevant
cosmological terms, which appear in the metrics. Connecting the metrics to a
new geometric definition of a charged Black Hole, we numerically investigate
the effective potentials of the total dynamical system, considering massive and
massless test particles, moving on such Black Holes.Comment: 8 pages, 5 figure
A Kinematical Approach to Conformal Cosmology
We present an alternative cosmology based on conformal gravity, as originally
introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas.
Unlike past similar attempts our approach is a purely kinematical application
of the conformal symmetry to the Universe, through a critical reanalysis of
fundamental astrophysical observations, such as the cosmological redshift and
others. As a result of this novel approach we obtain a closed-form expression
for the cosmic scale factor R(t) and a revised interpretation of the space-time
coordinates usually employed in cosmology. New fundamental cosmological
parameters are introduced and evaluated. This emerging new cosmology does not
seem to possess any of the controversial features of the current standard
model, such as the presence of dark matter, dark energy or of a cosmological
constant, the existence of the horizon problem or of an inflationary phase.
Comparing our results with current conformal cosmologies in the literature, we
note that our kinematic cosmology is equivalent to conformal gravity with a
cosmological constant at late (or early) cosmological times. The cosmic scale
factor and the evolution of the Universe are described in terms of several
dimensionless quantities, among which a new cosmological variable delta emerges
as a natural cosmic time. The mathematical connections between all these
quantities are described in details and a relationship is established with the
original kinematic cosmology by L. Infeld and A. Schild. The mathematical
foundations of our kinematical conformal cosmology will need to be checked
against current astrophysical experimental data, before this new model can
become a viable alternative to the standard theory.Comment: Improved version, with minor changes. 58 pages, including 7 figures
and one table. Accepted for publication in General Relativity and Gravitation
(GERG
Higher Derivative Operators from Transmission of Supersymmetry Breaking on S_1/Z_2
We discuss the role that higher derivative operators play in field theory
orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz)
breaking of supersymmetry. Integrating out the bulk fields generates
brane-localised higher derivative counterterms to the mass of the brane (or
zero-mode of the bulk) scalar field, identified with the Higgs field in many
realistic models. Both Yukawa and gauge interactions are considered and the
one-loop results found can be used to study the ``running'' of the scalar field
mass with respect to the momentum scale in 5D orbifolds. In particular this
allows the study of the behaviour of the mass under UV scaling of the momentum.
The relation between supersymmetry breaking and the presence of higher
derivative counterterms to the mass of the scalar field is investigated. This
shows that, regardless of the breaking mechanism, (initial) supersymmetry
cannot, in general, prevent the emergence of such operators. Some implications
for phenomenology of the higher derivative operators are also presented.Comment: 29 pages, LaTeX. Added Section 4 ("Phenomenological implications:
living with ghosts?") and Appendix
A class of elementary particle models without any adjustable real parameters
Conventional particle theories such as the Standard Model have a number of
freely adjustable coupling constants and mass parameters, depending on the
symmetry algebra of the local gauge group and the representations chosen for
the spinor and scalar fields. There seems to be no physical principle to
determine these parameters as long as they stay within certain domains dictated
by the renormalization group. Here however, reasons are given to demand that,
when gravity is coupled to the system, local conformal invariance should be a
spontaneously broken exact symmetry. The argument has to do with the
requirement that black holes obey a complementarity principle relating ingoing
observers to outside observers, or equivalently, initial states to final
states. This condition fixes all parameters, including masses and the
cosmological constant. We suspect that only examples can be found where these
are all of order one in Planck units, but the values depend on the algebra
chosen. This paper combines findings reported in two previous preprints, and
puts these in a clearer perspective by shifting the emphasis towards the
implications for particle models.Comment: 28 pages (incl. title page), no figure
Compactifications of conformal gravity
We study conformal theories of gravity, i.e. those whose action is invariant
under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is
well known, in order to obtain Einstein gravity in 4D it is necessary to
introduce a scalar compensator with a VEV that spontaneously breaks the
conformal invariance and generates the Planck mass. We show that the
compactification of extra dimensions in a higher dimensional conformal theory
of gravity also yields Einstein gravity in lower dimensions, without the need
to introduce the scalar compensator. It is the field associated with the size
of the extra dimensions (the radion) who takes the role of the scalar
compensator in 4D. The radion has in this case no physical excitations since
they are gauged away in the Einstein frame for the metric. In these models the
stabilization of the size of the extra dimensions is therefore automatic.Comment: 13 page
Energy in Generic Higher Curvature Gravity Theories
We define and compute the energy of higher curvature gravity theories in
arbitrary dimensions. Generically, these theories admit constant curvature
vacua (even in the absence of an explicit cosmological constant), and
asymptotically constant curvature solutions with non-trivial energy properties.
For concreteness, we study quadratic curvature models in detail. Among them,
the one whose action is the square of the traceless Ricci tensor always has
zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired
Einstein-Gauss-Bonnet model and show that both its flat and Anti-de-Sitter
vacua are stable.Comment: 18 pages, typos corrected, one footnote added, to appear in Phys.
Rev.
Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk
An analysis of a spherically symmetric braneworld configuration is performed
when the intrinsic curvature scalar is included in the bulk action; the
vanishing of the electric part of the Weyl tensor is used as the boundary
condition for the embedding of the brane in the bulk. All the solutions outside
a static localized matter distribution are found; some of them are of the
Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior
solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior,
while the other does not. A non-universal gravitational constant arises,
depending on the density of the considered object; however, the conventional
limits of the Newton's constant are recovered. An upper bound of the order of
TeV for the energy string scale is extracted from the known solar system
measurements (experiments). On the contrary, in usual brane dynamics, this
string scale is calculated to be larger than TeV.Comment: 23 pages, 1 figure, one minor chang
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