arXiv subjects
Publications and source records attributed to J. C. Rojas.
Using the Hamiltonian formulation, in terms of collective variables, we explore the evolution of different skyrmionic parameters as function of the isospin chemical potential ($μ$), such as the energy density, the charge density, the isoscalar radius and the isoscalar magnetic radius. We found that the radii start to grow very fast for $μ\gtrsim 140$ MeV, suggesting the occurrence of a phase transition.
In this letter we make use of the Background Field Method (BFM) to compute the effective potential of an SU(2) gauge field theory, in the presence of chemical potential and temperature. The main idea is to consider the chemical potential as the background field. The gauge fixing condition required by the BFM turns out to be exactly the one we found in a previous article in a different context.
We present a complete analysis of the Heavy Quark Effective Theory Lagrangian at order $1/m^2$ in the leading logarithmic approximation, including effects induced by spectator quarks. At this order new correction terms appear in the effective Lagrangian, as four-quark operators containing both heavy and light quark fields. We compute the coefficients of these operators to one-loop order and in the leading-logarithmic approximation. Two of them break the heavy quark spin symmetry and we estimate their contribution to the hyperfine splitting of the heavy mesons in the factorization approximation. We find that they make a positive contribution to the hyperfine splitting of about 10% of the measured splitting in the charm case and of up to 5% in the bottom case.
We discuss the stability of the Skyrmion solution in the presence of a finite isospin chemical potential $μ$. Solving numerically the mass of the Skyrmion as function of $μ$, we find a critical value $μ_c=222.8$ MeV where the Skyrmion mass vanishes. We compare the exact numerical treatment with an analytical discussion based on a special shape for the profile of the Skyrmion due to Atiyah and Manton. The extension of this ansatz for finite $μ$ works quite well for $μ<121$ MeV. Then, for small values of $μ$, where the analytical approach is valid, we consider the possibility of having an angular deformation for the Skyrmionic profile, which is possible for finite values of $μ$. This is however, a small effect. Finally we introduce finite temperature corrections, which strength the instability induced by the chemical potential, finding the dependence of the critical temperature on $μ$.
We present a new gauge fixing condition for the Weinberg-Salam electro-weak theory at finite temperature and density. After spontaneous symmetry breaking occurs, every unphysical term in the Lagrangian is eliminated with our gauge fixing condition. A new and simple Lagrangian can be obtained where we can identify the propagators and vertices. Some consequences are discussed, as the new gauge dependent masses of the gauge fields and the new Faddeev-Popov Lagrangian. After obtaining the quadratic terms, we calculate exactly the 1-loop effective potential identifying the contribution of every particular field.
We analyze the stability of different topological solutions in Quantum Field Theory when an isospin chemical potential $μ$ is included. We work in the limit when temperature vanishes. We find that static vortex solutions in $2+1D$ do exist. However, the 't Hooft-Polyakov monopole in $3+1D$ is no longer stable, as soon as the chemical potential acquires a finite value. In the case of the Skyrmion, this topological solution still exists for finite $μ$, up to a certain critical value.
The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound $θ\sim [ 10 {TeV}]^{-2}$ is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov- Bohm effect is also discussed.
The possibility of detecting noncommutive space relics is analyzed by using the Aharonov-Bohm effect. If space is non-commutative, it turns out that the holonomy receives kinematical corrections that tend to diffuse the fringe pattern. This fringe pattern has a non-trivial energy dependence and, therefore, one could observe noncommutative effects by modifying the energy of the incident electrons beam in the Tonomura experimental arrangement
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($θ$) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of $θ$ and for non-polynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $θ$, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction $V(r)$ is replaced by $V = V ({\hat H}_{HO}, {\hat L}_z)$, where ${\hat H}_{HO}$ is the hamiltonian of the two-dimensional harmonic oscillator and ${\hat L}_z$ is z- component of the angular momentum. For other finite values of $θ$ the model can be solved by using perturbation theory.
The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= Ω\aleph$ with $\aleph$ defined in the text, then for the value ${\tilde θ} = 0.22 \times 10^{-11} cm^2$ (that measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find differents values for ${\tilde θ}$ and, therefore, the possible bounds for ${\tilde θ}$ should be searched in a physical independent scenario. This last fact could explain the differents bounds for $\tilde θ$ found in the literature.
Assuming triviality of the 4-dimensional $λϕ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a stability condition for the gap-equation for the plasma mass. It shows a second order phase transition at zero temperature, in agreement with a large amount of analytical and RG analysis as well as Monte Carlo numerical evidence. As the cutoff $Λ$ is removed the renormalized self coupling constant $λ_R$ goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.