24 research outputs found
Gauge Fixing in Higher Derivative Gravity
Linearized four-derivative gravity with a general gauge fixing term is
considered. By a Legendre transform and a suitable diagonalization procedure it
is cast into a second-order equivalent form where the nature of the physical
degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing
"third ghosts", characteristic to higher-derivative theories, is made explicit.
The symmetries of the theory and the structure of the compensating
Faddeev-Popov ghost sector exhibit non-trivial peculiarities.Comment: 21 pages, LaTe
Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost
We prove that the linear instability in a non-degenerate higher derivative
theory, the Ostrogradski instability, can only be removed by the addition of
constraints if the original theory's phase space is reduced.Comment: 17 pages, no figures, version published in JCA
Ostrogradski Formalism for Higher-Derivative Scalar Field Theories
We carry out the extension of the Ostrogradski method to relativistic field
theories. Higher-derivative Lagrangians reduce to second differential-order
with one explicit independent field for each degree of freedom. We consider a
higher-derivative relativistic theory of a scalar field and validate a powerful
order-reducing covariant procedure by a rigorous phase-space analysis. The
physical and ghost fields appear explicitly. Our results strongly support the
formal covariant methods used in higher-derivative gravity.Comment: 22 page
Tensor Perturbations in Quantum Cosmological Backgrounds
In the description of the dynamics of tensor perturbations on a homogeneous
and isotropic background cosmological model, it is well known that a simple
Hamiltonian can be obtained if one assumes that the background metric satisfies
Einstein classical field equations. This makes it possible to analyze the
quantum evolution of the perturbations since their dynamics depends only on
this classical background. In this paper, we show that this simple Hamiltonian
can also be obtained from the Einstein-Hilbert lagrangian without making use of
any assumption about the dynamics of the background metric. In particular, it
can be used in situations where the background metric is also quantized, hence
providing a substantial simplification over the direct approach originally
developed by Halliwell and Hawking.Comment: 24 pages, JHEP forma
Functional Lagrange formalism for time-non-local Lagrangians
We develop a time-non-local (TNL) formalism based on variational calculus,
which allows for the analysis of TNL Lagrangians. We derive the generalized
Euler-Lagrange equations starting from the Hamilton's principle and, by
defining a generalized momentum, we introduce the corresponding Hamiltonian
formalism. We apply the formalism to second order TNL Lagrangians and we show
that it reproduces standard results in the time-local limit. An example will
show how the formalism works, and will provide an interesting insight on the
non-standard features of TNL equations.Comment: 13 pages, 2 figure
A realisation of Lorentz algebra in Lorentz violating theory
A Lorentz non-invariant higher derivative effective action in flat spacetime,
characterised by a constant vector, can be made invariant under infinitesimal
Lorentz transformations by restricting the allowed field configurations. These
restricted fields are defined as functions of the background vector in such a
way that background dependance of the dynamics of the physical system is no
longer manifest. We show here that they also provide a field basis for the
realisation of Lorentz algebra and allow the construction of a Poincar\'e
invariant symplectic two form on the covariant phase space of the theory.Comment: text body edited, reference adde