Equivalence between the semiclassical and effective approaches to gravity

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantum mechanics versus equivalence principle

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle theta for a photon passing by the sun is evaluated afterward and the likelihood of detecting Delta theta/theta(E) theta-theta(E)/theta(E) (where theta(E) is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.

Testing the principle of equivalence by supernova neutrinos

We study the possible impact of the neutrino oscillation which could be induced by a tiny violation of equivalence principle (VEP) on the observation of neutrinos emitted from supernova driven by gravitational collapse. We show that using supernova neutrinos, one can probe very small values of VEP parameters, delta(tau) less than or similar to O(10(-31)) for massless or degenerated neutrinos and delta(tau) less than or similar to O(10(-16)) x (Deltam(2)/10(-5) eV(2)) for massive neutrinos. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

K-bi-Lipschitz equivalence of real function-germs

In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to K-bi-Lipschitz equivalence, is finite.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

CLASSICAL EQUIVALENCE OF LAMBDA-R-PHI-2 THEORIES

It is shown that the action functional S[g, phi] = integral d4 x square-root -g[R/k(1 + klambdaphi2) + partial derivative(mu)phi partial derivative(mu)phi] describes, in general, one and the same classical theory whatever may be the value of the coupling constant lambda.

Reduced Insulin Secretion in Protein Malnourished Mice Is Associated with Multiple Changes in the beta-Cell Stimulus-Secretion Coupling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the equivalence of the mechanisms governing switching and hysteresis phenomena

The nucleation and growth model, which is usually applied to switching phenomena, is adapted for explaining surface potential measurements on the P(VDF-TrFE) (polyvinylidene fluoride-trifluoroethylene) copolymer obtained in a constant current corona triode. It is shown that the growth is one-dimensional and that the nucleation rate is unimportant, probably because surface potential measurements take much longer than the switching ones. The surface potential data can therefore be accounted for by a growth model in which the velocity of growth varies exponentially with the electric field. Since hysteresis loops can be obtained from surface potential measurements, it is suggested that similar mechanisms can be used when treating switching and hysteresis phenomena, provided that account is taken of the difference in the time scale of the measurements.

Remarks on fermion-boson equivalence in three dimensions

Starting from a decomposition of the self-dual field in (2 + 1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it with the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in 1/m. Some problems related to the number of poles of the effective propagator are also addressed.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

Equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations

A strict proof of the equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon Fock theories is presented for physical S-matrix elements in the case of charged scalar particles minimally interacting with an external or quantized electromagnetic field. The Hamiltonian canonical approach to the Duffin - Kemmer Petiau theory is first developed in both the component and the matrix form. The theory is then quantized through the construction of the generating functional for the Green's functions, and the physical matrix elements of the S-matrix are proved to be relativistic invariants. The equivalence of the two theories is then proved for the matrix elements of the scattered scalar particles using the reduction formulas of Lehmann, Symanzik, and Zimmermann and for the many-photon Green's functions.

Classical versus quantum equivalence between sine-Gordon, Liouville and other solitons

In this work we present a mapping between the classical solutions of the sine-Gordon, Liouville, λφ4 and other kinks in 1+1 dimensions. This is done by using an invariant quantity which relates the models. It is easily shown that this procedure is equivalent to that used to get the so called deformed solitons, as proposed recently by Bazeia et al. [Phys. Rev. D. 66 (2002) 101701(R)]. The classical equivalence is explored in order to relate the solutions of the corresponding models and, as a consequence, try to get new information about them. We discuss also the difficulties and consequences which appear when one tries to extend the deformation in order to take into account the quantum version of the models.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.