30 research outputs found
Higher-Derivative Boson Field Theories and Constrained Second-Order Theories
As an alternative to the covariant Ostrogradski method, we show that
higher-derivative relativistic Lagrangian field theories can be reduced to
second differential-order by writing them directly as covariant two-derivative
theories involving Lagrange multipliers and new fields. Despite the intrinsic
non-covariance of the Dirac's procedure used to deal with the constraints, the
explicit Lorentz invariance is recovered at the end. We develop this new
setting on the grounds of a simple scalar model and then its applications to
generalized electrodynamics and higher-derivative gravity are worked out. For a
wide class of field theories this method is better suited than Ostrogradski's
for a generalization to 2n-derivative theoriesComment: 31 pages, Plain Te
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
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
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