arXiv subjects

Nuno Barros e Sa

Publications and source records attributed to Nuno Barros e Sa.

7 recordsLinked to original sources

arXiv2012

Families of complex Hadamard matrices

What is the dimension of a smooth family of complex Hadamard matrices including the Fourier matrix? We address this problem with a power series expansion. Studying all dimensions up to 100 we find that the first order result is misleading unless the dimension is 6, or a power of a prime. In general the answer depends critically on the prime number decomposition of the dimension. Our results suggest that a general theory is possible. We discuss the case of dimension 12 in detail, and argue that the solution consists of two 13-dimensional families intersecting in a previously known 9-dimensional family. A precise conjecture for all dimensions equal to a prime times another prime squared is formulated.

math-ph↗

arXiv2009

Vacuum Stability in two-Higgs doublet models

In this work we review the status of tree-level vacuum stability in general two-Higgs doublet models. We also discuss the problem of Normal minima in some classes of potentials. In some of these potentials, Normal minima can coexist leading to potentially dangerous physic scenarios as, for instance, a two step spontaneous symmetry breaking.

hep-ph↗

arXiv2000

Uncertainty for spin systems

A modified definition of quantum mechanical uncertainty D for spin systems, which is invariant under the action of SU(2), is suggested. Its range is shown to be h^2j<D<h^2j(j+1) within any irreducible representation j of SU(2) and its mean value in Hilbert space computed using the Fubini-Study metric is determined to be mean(D)=h^2j(j+1/2). The most used sets of coherent states in spin systems coincide with the set of minimum D uncertainty states.

quant-ph↗

arXiv2000

Decomposition of Hilbert space in sets of coherent states

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups. The group SU(2) is studied in particular and the orbit spaces of its j=1/2 and j=1 representations completely determined. The orbits of SU(2) in CP^N can be either 2 or 3 dimensional, the first of them being either isomorphic to S^2 or to RP^2 and the latter being isomorphic to quotient spaces of RP^3. We end with a look from the same perspective to the quantum mechanical space of states in particle mechanics.

quant-ph↗

arXiv2000

Hamiltonian analysis of General relativity with the Immirzi parameter

Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints, presenting the theory with a Hamiltonian composed of first class constraints which are the generators of the gauge symmetries of the action. In the time gauge we then recover Barbero's formulation of gravity.

gr-qc↗

arXiv2000

A note on topological brane theories

We consider the theory of closed $p$-branes propagating on $(p+1)$-dimensional space-time manifolds. This theory has no local degrees of freedom. Here we study its canonical and BRST structures of the theory. In the case of locally flat backgrounds one can show that the $p$-brane theory is related to another known topological field theory. In the general situation some equivalent actions can also be written for the topological $p$-brane theory.

hep-th↗

arXiv1997

Geodesics or autoparallels from a variational principle?

Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The purpose of this letter is to call attention to the problems that such attempts raise, namely the requirement of a more elaborate structure in order to formulate the variational principle and the lack of a Hamiltonian description for the autoparallel motion. Here is also raised the problem of how to generalize this proposed new principle to quantum mechanics and to field theory. Since all applications known of such a principle are equally well described in terms of geodesics in non-holonomic frames we conclude that there is no reason to modify the conventional variational principle that leads to geodesics.

gr-qc↗