Covariant quantization of the superstring

After constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor ghost variable, the superstring is covariantly quantized and N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. © 2004 Published by Elsevier B.V.

Consistency between light-front quantization and covariantization for zero modes

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional spurious or unphysical pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory. © World Scientific Publishing Company.

On superfield covariant quantization in general coordinates

We propose a natural extension of the BRST-antiBRST superfield covariant scheme in general coordinates. Thus, the coordinate dependence of the basic tensor fields and scalar density of the formalism is extended from the base supermanifold to the complete set of superfield variables. © Springer-Verlag.

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the generalized scalar electrodynamics (GSQED4). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, we present the computation and further discussion on the radiative correction at α order; and, as it turns out, an unexpected mP-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, we also give a diagrammatic discussion on the photon self-energy at α2 order, where we observe contributions from the meson self-energy function. Afterwards, we present the expressions of the counterterms and effective coupling of the theory, obtaining from the latter an energy range where the theory is defined by m2≤k2

Férmions em referenciais acelerados: desintegração de prótons e outras aplicações

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

Quantization of unstable linear scalar fields in static spacetimes

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

Markovian versus non-Markovian stochastic quantization of a complex-action model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A quantum theory for the excitation spectrum of a rectangular Andreev billiard

We consider a N - S box system consisting of a rectangular conductor coupled to a superconductor. The Green functions are constructed by solving the Bogoliubov-de Gennes equations at each side of the interface, with the pairing potential described by a step-like function. Taking into account the mismatch in the Fermi wave number and the effective masses of the normal metal - superconductor and the tunnel barrier at the interface, we use the quantum section method in order to find the exact energy Green function yielding accurate computed eigenvalues and the density of states. Furthermore, this procedure allow us to analyze in detail the nontrivial semiclassical limit and examine the range of applicability of the Bohr-Sommerfeld quantization method.

Canonical Quantization of a Massive Weyl Field

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed.

Stochastic quantization of the spherical model and supersymmetry.

In this work, we reported some results about the stochastic quantization of the spherical model. We started by reviewing some basic aspects of this method with emphasis in the connection between the Langevin equation and the supersymmetric quantum mechanics, aiming at the application of the corresponding connection to the spherical model. An intuitive idea is that when applied to the spherical model this gives rise to a supersymmetric version that is identified with one studied in Phys. Rev. E 85, 061109, (2012). Before investigating in detail this aspect, we studied the stochastic quantization of the mean spherical model that is simpler to implement than the one with the strict constraint. We also highlight some points concerning more traditional methods discussed in the literature like canonical and path integral quantization. To produce a supersymmetric version, grounded in the Nicolai map, we investigated the stochastic quantization of the strict spherical model. We showed in fact that the result of this process is an off-shell supersymmetric extension of the quantum spherical model (with the precise supersymmetric constraint structure). That analysis establishes a connection between the classical model and its supersymmetric quantum counterpart. The supersymmetric version in this way constructed is a more natural one and gives further support and motivations to investigate similar connections in other models of the literature.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Using the Franck-Hertz Experiment To Illustrate Quantization Energy States of the Neon Atom by Electron Impact

na provide students with motivation for the study of quantum mechanics. That microscopic matter exists in quantized states can be demonstrated with modem versions of historic experiments: atomic line spectra (I), resonance potentials, and blackbody radiation. The resonance potentials of mercury were discovered by Franck and Hertz in 1914 (2). Their experiment consisted of bombarding atoms by electrons, and detecting the kinetic energy loss of the scattered electrons (3). Prior to the Franck-Hertz experiment, spectroscopic work bv Balmer and Rvdbere revealed that atoms emitted radiatibn at discrete ekergiis. The Franck-Hertz experiment showed directly that auantized enerm levels in an atom are real, not jist optiEal artifacts. atom can be raised to excited states by inelastic collisions with electrons as well as lowered from excited states by emission of photons. The classic Franck-Hertz experiment is carried out with mercury (4-7). Here we present an experiment for the study of resonance potentials using neon.