Educação matemática pela arte
Gusmão, Lucimar Donizete
2013-08-28
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225 records were found.
In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It has been known for a long time that the propagator of such a scalar field diverges at the lower end of the integration over the momenta when evaluated for the Bunch-Davies vacuum. The resolution we propose to this problem is to work on a spatially compact universe. This effectively generates an infrared cut-off in the integral over the mode functions. To see what the physical effect of this approaches is, we calculated the expectation value of the stress energy tensor. Using the infrared regulated propagator, we find in the ultraviolet that we...
In this PhD thesis we have studied the production of massive particles at the Large Hadron Collider (LHC). We found very large corrections that can be compared with experimental results. The LHC is a big particle accelerator at CERN, Geneva where protons are collided against each other. After such high-energy proton collisions, different particles are produced, including massive particles. The experimentalists measure the cross section, which is related to the production rate, that specific massive particles are produced which are then subsequently compared with theoretical predictions from the theory called Quantum Chromodynamics (QCD). Because of the large mass of these particles, they have a small velocity after being produced and it can be shown in QCD that the cross section for their production can be expressed as a series in larg...
An alternative to the usual vierbein field in a (3 + 1)-dimensional (euclidean) space-time is proposed such that the internal index takes only three values and the external is a double: ea = −ea. In flat space-time this field reduces to the self-dual generalized Levi-Civita symbol a. Like the vierbein field, our field determines the metric field g uniquely. It can be viewed upon as the 'cube root' of the metric field. In euclidean space the internal symmetry group is SL(3). In Minkowski space, in a sense to be explained, the internal symmetry group is SU(3).
The Einstein-Hilbert action takes an elegant form in terms of this new field.
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to des...
Comment: Correction of formula in Appendix, and extra references added
One-loop Feynman diagrams, when regularized using the continuous dimension method, exhibit single poles at n = 4, and these poles can be eliminated by a counterterm Ä in the Lagrangian. In this paper a simple algorithm is derived to express Ä in terms of the components of the Lagrangian without performing integrations. It can be used in dimensional regularization, but also to derive Callan-Symanzik type equations for small distance behaviour in any renormalizable
The gravitational force harbours a fundamental instability against collapse. In standard General Relativity without Quantum Mechanics, this implies the existence of black holes as natural, stable solutions of Einstein's equations. If one attempts to quantize the gravitational force, one should also consider the question how Quantum Mechanics affects the behaviour of black holes. In this lecture, we concentrate on the horizon. One would have expected that its properties could be derived from general coordinate transformations out of a vacuum state. In contrast, it appears that much new physics is needed. Much of that is still poorly understood, but one may speculate on the way information is organized at a horizon, and how refined versions of Quantum Theory may lead to answers.
