Repositório Digital

The goal is to help you to organise your research and to succeed while making the process as personalised and convenient as possible for you. We present our ideas as guidelines on several major topics related to building, working, writing, presenting, and surviving an academic journey. The advice is divided by respective chapters, and you can choose either to follow the proposed order or jump around, depending on where you are on your journey. We present what went right and wrong for us, and ...

We present a simple proof that self-avoiding fermionic strings solutions solve formally (in a Quantum Mechanical Framework) the $QCD(U(N_c))$ Loop Wave Equation written in terms of random loops.

Indecomposable positive energy quantum matter comes in 3 forms: one massive and two massless families of which about the so called "infinite spin" family was little known up to recently. Using novel methods which are particularly suited for problems of localization, it was shown that this quantum matter of the third kind cannot be generated by pointlke localized fields but rather needs semiinfinite stringlike generators. Arguing that the field algebras generated by these new objects do not po...

We discuss the quantization of a class of relativistic fluid models defined in terms of one real and two complex conjugate potentials with values on a Kähler manifold, and parametrized by the Kähler potential $K(z, \overline{z})$ and a real number $\lambda$. In the hamiltonian formulation, the canonical conjugate momenta of the potentials are subjected to second class constraints which allow us to apply the symplectic projector method in order to find the physical degrees of freedom and the p...

We furnish an algebraic understanding of the inequivalent connectivities (computed up to N -

In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably decreases. The algorithm is based on a graphic representation and, when the corresponding graph is drawn, coordinate pairs will originate two straight lines that intercept one another. These coordinate pairs are formed by prime numbers in the x-axis, and fact...