Quantum properties of the Dirac field on BTZ black hole backgrounds

We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty}(r_+,\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1 + 2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.Comment: 19 pages; IOP styl

Quantum properties of the electron field in Kerr-Newman black hole manifolds

We study some spectral features of the one-particle electron Hamiltonian obtained by separating the Dirac equation in a Kerr-Newman black hole background. We find that the essential spectrum includes the whole real line. As a consequence, there is no gap in the spectrum and discrete eigenvalues are not allowed for any value of the black hole charge $Q$ and angular momentum $J$. Our spectral analysis will be also related to the dissipation of the black hole angular momentum and charge.Comment: 9 pages, uses revte

Quantum Models of Black Hole Evaporation

The discovery of black-hole evaporation represented in many respects a revolutionary event in scientific world; as such, in giving answers to open questions, it gave rise to new problems part of which are still not resolved. Here we want to make a brief review of such problems and examine some possible solutions. Invited Talk at the "Workshop on String Theory, Quantum Gravity and the Unification of the Fundamental Interactions" Rome, September 21-26Comment: 9 pages, ROM2F-92/6

A Conformal Affine Toda Model of 2D Black Holes: A Quantum Study of the Evaporation End-Point

In this paper we reformulate the dilaton-gravity theory of Callan \etal\ as a new effective conformal field theory which turns out to be a generalization of the so-called $SL_2$-conformal affine Toda (CAT) theory studied some times ago by Babelon and Bonora. We quantize this model, thus keeping in account the dilaton-gravity quantum effects. We then implement a Renormalization Group analysis to study the black hole thermodynamics and the final state of the Hawking evaporation.Comment: 15 pages, phyzzx, ROM-2F-92-5

Phi-Psi model for Electrodynamics in dielectric media: exact quantisation in the Heisenberg representation

We investigate the quantization in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field $\phi$ and the role of the polarization field is played by a further scalar field $\psi$. The model, which is quadratic in the fields, is still characterized by a nontrivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction representation is also considered.Comment: 9 page

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.Comment: 24 page

Path integral quantization of the relativistic Hopfield model

The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path integral formalism. In particular we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.Comment: 16 page

Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background

We consider the Dirac equation on the background of a Kerr-Newman-de Sitter black hole. By performing variable separation, we show that there exists no time-periodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previously considered cases, the novelty is represented by the presence, together with a black hole event horizon, of a cosmological (non degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case.Comment: 12 pages. AMS styl

A CONTRIBUTION TO THE STUDY OF A PISA ALLUVIAL PLAIN SECTOR FOR LOW TEMPERATURE GEOTHERMAL ASSESSMENT

The target of this work is to evaluate the possible feeding of the east sector of the Pisa plain hydrogeological system by the Monte Pisano meteoric waters, using a geochemical and geological approach. The study was made considering the Calci basin and the area of the sedimentary plain adjacent at the Calci fan, where spring and well waters have been sampled and analyzed. The analyses of the major and minor elements of the well waters have confirmed a common origin with the springs above the Calci major alluvial fan, showing the same geochemical fingerprint. The isotopic analyses (δD-δ18O) allowed to compute the average altitude of infiltration of the waters. The altitudes obtained for the groundwaters sampled close to the alluvial fan are comparable with the average altitude of the Monte Pisano, confirming the hypothesis of the feeding of this aquifer sector by the Calci alluvial fan. The meteoric waters infiltrate through the debris-alluvial bodies that cover the south-western side of the Monte Pisano slopes reaching the aquifers at the foot of the hills. A possible water contribution to the feeding of about 5*106 m3/yr has been estimated from the hydrologic budget of the drainage basin above the Calci alluvial fan