Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure

Complex Moduli of Physical Quanta

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold are often not unique. This letter is devoted to analysing the dependence of the notion of a quantum on the complex-differentiable structure chosen on classical phase space.Comment: Some minor cosmetic changes made and new refs. adde

Canonical and gravitational stress-energy tensors

It is dealt with the question, under which circumstances the canonical Noether stress-energy tensor is equivalent to the gravitational (Hilbert) tensor for general matter fields under the influence of gravity. In the framework of general relativity, the full equivalence is established for matter fields that do not couple to the metric derivatives. Spinor fields are included into our analysis by reformulating general relativity in terms of tetrad fields, and the case of Poincare gauge theory, with an additional, independent Lorentz connection, is also investigated. Special attention is given to the flat limit, focusing on the expressions for the matter field energy (Hamiltonian). The Dirac-Maxwell system is investigated in detail, with special care given to the separation of free (kinetic) and interaction (or potential) energy. Moreover, the stress-energy tensor of the gravitational field itself is briefly discussed.Comment: final version, to appear in Int. J. Mod. Phys.

Feedback-limited Accretion: Luminous Signatures from Growing Planets

Planets form in discs of gas and dust around stars, and keep growing by accretion of disc material while available. Massive planets clear a gap in that protoplanetary disc, but still accrete through spiral wakes. On its way to the planet, the gas will settle on a \emph{circumplanetary} disc around the planet and slowly accrete on to it. The energy of the accreted gas will be released, heating the planet surroundings in a feedback process. For high enough accretion rates the planet should be detectable at infrared wavelengths. We aim to find whether detectable planet luminosities, $\gtrsim 10^{-3} \, \textrm{L}_\odot$, can occur when considering that the planet luminosity is coupled to the accretion, and also to study which other effects has the feedback on the dynamics of the circumplanetary and the gap regions. We model a planet with mass ratio $q=10^{-3}$, orbiting at 10 AU from a solar mass star, using a modified version of the 2D code FARGO-AD, which includes a prescription for the accretion and feedback luminosity of the planet. We find that the planetary feedback is able to partially deplete the circumplanetary disc, and to reduce the accretion rate onto the planet. However, detectable luminosities of $L_\textrm{p}\gtrsim 10^{-3}\, \textrm{L}_\odot$ are still produced. The feedback also contributes to partially refilling the gap, to heat up the coorbital region, and to perturb the orbital velocity of the gas.Comment: Submitted to MNRA

Time without time: a stochastic clock model

We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasi-local observables which measure the system's ``change'' in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and Fisher-Rao information metric. The emergent reparametrization-invariant ``time'' does not run smoothly but is simply related to the proper time on the average. For sufficiently low energy, the external motion is then described by a unitary quantum mechanical evolution in accordance with the Schr\"odinger equation.Comment: 18 pages; LaTeX. 4 (.ps) plus 2 (.gif) figure file

Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has been already studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR action) it is in the constraint on the B fields. In this work we continue the analysis of their relationship but at the Hamiltonian level. Particularly, we are interested in seeing how the above difference appears in the constraint structure of both action principles. We find that they both possess the same number of first-class and second-class constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on account of the type of canonical variables employed. The two algebras can be transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the corrections to many misprints of v1 and also the ones of the published version. The conceptual and technical parts of the paper are not altere