160 research outputs found
Gauge fixing in higher derivative field theories
Higher Derivative (HD) Field Theories can be transformed into second order
equivalent theories with a direct particle interpretation. In a simple model
involving abelian gauge symmetries we examine the fate of the possible gauge
fixings throughout this process. This example is a useful test bed for HD
theories of gravity and provides a nice intuitive interpretation of the "third
ghost" occurring there and in HD gauge theories when a HD gauge fixing is
adopted.Comment: 16 pages, Latex,( Preprint imaff 93/10
Common Challenges Faced By Rural Principals: A Review of the Literature
Within this article, we thematically present common challenges associated with the role of the rural principal. In this literature review, we delimit our search to work published from 2003–2013. A limitation of this study is that it represents data predominantly from American, Canadian, and Australian rural settings, restricting a global applicability of results. Findings highlight that many rural principal candidates face a hiring disadvantage if they do not have a historical connection with the community advertising a position. Additional challenges include juggling diverse responsibilities, lack of professional development and resources, gender discrimination, and issues surrounding school accountability and change. This information is beneficial for researchers, policymaker, senior educational leaders, principals, vice-principals, teachers, parents, and community members interested in school leadership within rural communities. We conclude that to be successful, rural principals must be able to nimbly mediate relations within the local community and the larger school system
Four-Dimensional Higher-Derivative Supergravity and Spontaneous Supersymmetry Breaking
We construct two classes of higher-derivative supergravity theories
generalizing Einstein supergravity. We explore their dynamical content as well
as their vacuum structure. The first class is found to be equivalent to
Einstein supergravity coupled to a single chiral superfield. It has a unique
stable vacuum solution except in a special case, when it becomes identical to a
simple no-scale theory. The second class is found to be equivalent to Einstein
supergravity coupled to two chiral superfields and has a richer vacuum
structure. It is demonstrated that theories of the second class can possess a
stable vacuum with vanishing cosmological constant that spontaneously breaks
supersymmetry. We present an explicit example of this phenomenon and compare
the result with the Polonyi model.Comment: 26 pages, LaTeX2e and AMS-LaTeX 1.2, 1 eps figur
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
Non-Trivial Vacua in Higher-Derivative Gravitation
A discussion of an extended class of higher-derivative classical theories of
gravity is presented. A procedure is given for exhibiting the new propagating
degrees of freedom, at the full non-linear level, by transforming the
higher-derivative action to a canonical second-order form. For general
fourth-order theories, described by actions which are general functions of the
scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown
that the higher-derivative theories may have multiple stable vacua. The vacua
are shown to be, in general, non-trivial, corresponding to deSitter or
anti-deSitter solutions of the original theory. It is also shown that around
any vacuum the elementary excitations remain the massless graviton, a massive
scalar field and a massive ghost-like spin-two field. The analysis is extended
to actions which are arbitrary functions of terms of the form ,
and it is shown that such theories also have a non-trivial vacuum structure.Comment: 25 pages, LaTeX2e with AMS-LaTeX 1.2, 7 eps figure
Charged Black Holes In Quadratic Theories
We point out that in general the Reissner-Nordstr\"om (RN) charged black
holes of general relativity are not solutions of the four dimensional quadratic
gravitational theories. They are, e.g., exact solutions of the
quadratic theory but not of a theory where a term is present in
the gravitational Lagrangian. In the case where such a non linear curvature
term is present with sufficiently small coupling, we obtain an approximate
solution for a charged black hole of charge and mass . For the
validity of this solution extends down to the horizon. This allows us to
explore the thermodynamic properties of the quadratic charged black hole and we
find that, to our approximation, its thermodynamics is identical to that of a
RN black hole. However our black hole's entropy is not equal to the one fourth
of the horizon area. Finally we extend our analysis to the rotating charged
black hole and qualitatively similar results are obtained.Comment: 11 pages, LaTeX/RevTeX3.
Generalized Gravity and a Ghost
We show that generalized gravity theories involving the curvature invariants
of the Ricci tensor and the Riemann tensor as well as the Ricci scalar are
equivalent to multi- scalar-tensor gravities with four derivatives terms. By
expanding the action around a vacuum spacetime, the action is reduced to that
of the Einstein gravity with four derivative terms, and consequently there
appears a massive spin-2 ghost in such generalized gravity theories in addition
to a massive spin-0 field.Comment: 8 pages, a reference adde
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.
A new duality transformation for fourth-order gravity
We prove that for non-linear L = L(R), the Lagrangians L and \hat L give
conformally equivalent fourth-order field equations being dual to each other.
The proof represents a new application of the fact that the operator
is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
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