Matemática
https://hdl.handle.net/10669/280
2024-02-22T07:58:37ZCharacterization of principal bundles: the commutative case
https://hdl.handle.net/10669/90868
Characterization of principal bundles: the commutative case
A review of the characterization of principal bundles, through the different properties of the action of a group and its related canonical and translation maps, is presented. The work is divided in three stages: a topological group acting on a topological space, a discrete group acting on a smooth manifold, and a Lie group acting on a smooth manifold.
2023-10-04T00:00:00ZImproved Epstein-Glaser renormalization in x-space versus differential renormalization
https://hdl.handle.net/10669/90306
Improved Epstein-Glaser renormalization in x-space versus differential renormalization
Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
2014-09-01T00:00:00ZMetric properties of the fuzzy sphere
https://hdl.handle.net/10669/90168
Metric properties of the fuzzy sphere
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with these spectral distances, form a sequence of metric spaces that converge to the round sphere in the high-spin limit.
2013-02-01T00:00:00ZTesting one-body density functionals on a solvable model
https://hdl.handle.net/10669/90167
Testing one-body density functionals on a solvable model
There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent phase-space formalism, we thoroughly test some of the most popular of those functionals on a completely solvable model.
2012-10-01T00:00:00Z