147 research outputs found
Hamiltonization of theories with degenerate coordinates
We consider a class of Lagrangian theories where part of the coordinates does
not have any time derivatives in the Lagrange function (we call such
coordinates degenerate). We advocate that it is reasonable to reconsider the
conventional definition of singularity based on the usual Hessian and,
moreover, to simplify the conventional Hamiltonization procedure. In
particular, in such a procedure, it is not necessary to complete the degenerate
coordinates with the corresponding conjugate momenta.Comment: 14 pages, LaTex fil
Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser
We argue that the obstacles to having a first-order formalism for
odd-derivative actions presented in a pedagogical note by Deser are based on
examples which are not first-order forms of the original actions. The general
derivation of an equivalent first-order form of the original second-order
action is illustrated using the example of topologically massive
electrodynamics (TME). The correct first-order formulations of the TME model
keep intact the gauge invariance presented in its second-order form
demonstrating that the gauge invariance is not lost in the Ostrogradsky
process.Comment: 6 pages, references are adde
Ostrogradsky's Hamilton formalism and quantum corrections
By means of a simple scalar field theory it is demonstrated that the Lagrange
formalism and Ostrogradsky's Hamilton formalism in the presence of higher
derivatives, in general, do not lead to the same results. While the two
approaches are equivalent at the classical level, differences appear due to the
quantum corrections.Comment: 10 pages, 1 figure, REVTeX
Ghost-free higher-derivative theory
We present an example of the quantum system with higher derivatives in the
Lagrangian, which is ghost-free: the spectrum of the Hamiltonian is bounded
from below and unitarity is preserved.Comment: 13 pages, 1 figur
On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions
It is shown that the well-known triviality of the Einstein field equations in
two dimensions is not a sufficient condition for the Einstein-Hilbert action to
be a total divergence, if the general covariance is to be preserved, that is, a
coordinate system is not fixed. Consequently, a Hamiltonian formulation is
possible without any modification of the two dimensional Einstein-Hilbert
action. We find the resulting constraints and the corresponding gauge
transfromations of the metric tensor.Comment: 9 page
Spontaneously scalarized Kerr black holes in extended scalar-tensor-Gauss-Bonnet gravity
We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.publishe
Second Order Gauge Theory
A gauge theory of second order in the derivatives of the auxiliary field is
constructed following Utiyama's program. A novel field strength arises besides the one of the first order treatment, . The associated conserved current is obtained. It has a new
feature: topological terms are determined from local invariance requirements.
Podolsky Generalized Eletrodynamics is derived as a particular case in which
the Lagrangian of the gauge field is . In this application
the photon mass is estimated. The SU(N) infrared regime is analysed by means of
Alekseev-Arbuzov-Baikov's Lagrangian.Comment: 27 pages. No figure. Final versio
Gauge invariances of higher derivative Maxwell-Chern-Simons field theory -- a new Hamiltonian approach
A new method of abstracting the independent gauge invariances of higher
derivative systems, recently introduced in [1], has been applied to higher
derivative field theories. This has been discussed taking the extended
Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the
model is provided. This Hamiltonian analysis has been used to construct the
independent gauge generator. An exact mapping between the Hamiltonian gauge
transformations and the U(1) symmetries of the action has been established.Comment: 16 pages, no figure. Title and abstract modified, new references
added. This version to appear in Phys. Rev.
Cleaning up the cosmological constant
We present a novel idea for screening the vacuum energy contribution to the
overall value of the cosmological constant, thereby enabling us to choose the
bare value of the vacuum curvature empirically, without any need to worry about
the zero-point energy contributions of each particle. The trick is to couple
matter to a metric that is really a composite of other fields, with the
property that the square-root of its determinant is the integrand of a
topological invariant, and/or a total derivative. This ensures that the vacuum
energy contribution to the Lagrangian is non-dynamical. We then give an
explicit example of a theory with this property that is free from Ostrogradski
ghosts, and is consistent with solar system physics and cosmological tests.Comment: 8 pages, typos corrected and more text added, version accepted for
publication in JHE
Perturbative Hamiltonian constraints for higher order theories
We present a method for constructing a consistent low energy canonical
formalism for higher order time-derivative theories, extending the Dirac method
to include perturbative Hamiltonian constraints. We apply it to two
paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan
scalar field. We also compare the results, both at the classical and quantum
level, with the ones corresponding to a direct perturbative construction
applied to the exact higher order theory. This comparison highligths the
soundness of the present formalism.Comment: 26 pages, 4 figures; review section shortened and appendices change
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