Antonio Accioly

Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions

A prescription for computing the propagator for D-dimensional higher-derivative gravity theories, based on the Barnes–Rivers operators, is presented. A systematic study of the tree-level unitarity of these theories is developed and the agreement of their linearized versions with Newton’s law is investigated by computing the corresponding effective nonrelativistic potential. Three-dimensional quadratic gravity with a gravitational Chern–Simons term is also analyzed. A discussion on the issue of light bending within the framework of both D-dimensional quadratic gravity and three-dimensional quadratic gravity with a Chern–Simons term is provided as well.

Boson-boson effective nonrelativistic potential for higher-derivative electromagnetic theories in D dimensions

The problem of computing the effective nonrelativistic potential U{sub D} for the interaction of charged-scalar bosons, within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that U{sub 3} cannot bind a pair of identical charged-scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.

One And The Same Route: Two Outstanding Electrodynamics

We show that the same route that leads to Maxwells electrodynamics leads also to Podolskys electrodynamics, provided we start from Podolskys electrostatic force law instead of the usual Coulombs law.

Fierz-Pauli higher derivative gravity

We consider a model for gravity in which the linear part of the four-derivative terms oRmn Rmn d4 x and oR2 d4 x are included into the Fierz-Pauli gravitational action. Unitarity is discussed at the tree-level. The issue of the gravitational deflection of a light ray is also considered.

Conformal coupling and Foldy-Wouthuysen transformation

The propagation of a free scalar field ϕ with mass m in a curved background is generally described by the equation (gμν∇μ∇ν + m2 + ξR)ϕ = 0. There exist some arguments in the literature that seem to favor the conformal coupling to the detriment of the minimal one. However, the majority of these claims are inconclusive. Here we show that the exact Foldy–Wouthuysen transformation for spin-0 particle coupled to a wide class of static spacetime metrics exists independently of the value of ξ. Nevertheless, if the coupling is of the conformal type, the gravitational Darwin-like term has an uncomplicated structure and it is proportional to the corresponding term in the fermionic case. In addition, an independent computation of this term, which has its origin in the zitterbewegung fluctuation of the bosons position with the mean square ≈ 1/m2, gives a result that coincides with that obtained using the aforementioned exact transformation with ξ = 1/6.

Is it physically sound to add a topologically massive term to three-dimensional massive electromagnetic or gravitational models?

The addition of a topologically massive term to an admittedly nonunitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its nonunitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, cannot coexist from the viewpoint of unitarity with topologically massive terms. We also discuss the novel features of the three-term effective field models that are gauge-invariant.

UNAVOIDABLE CONFLICT BETWEEN MASSIVE GRAVITY MODELS AND MASSIVE TOPOLOGICAL TERMS

Massive gravity models in (2+1) dimensions, such as those obtained by adding to Einsteins gravity the usual Fierz–Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern–Simons term. Furthermore, if the massive topological term is added to

PHOTON MASS and VERY LONG BASELINE INTERFEROMETRY

R+R_{\mu\nu}^2

Gravitational rainbow of massive particles

gravity, or to

Bending of light in the framework of R + R2 gravity

R+R_{\mu\nu}^2+R^2