Quantum-Mechanical Dualities from Classical Phase Space

The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum with respect to an observer on C. We illustrate this property explicitly in the case when classical phase space is complex n-dimensional projective space. We also provide some examples of classical dynamics that exhibit these properties at the quantum level.Comment: 8 pages, Late

Quantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe

Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/h), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a point-by-point basis on configuration space. This is equivalent to the statement that quantum mechanics is a U(1) gauge theory. Unlike Yang-Mills theories, however, the geometry of this gauge symmetry is not given by a fibre bundle, but rather by a gerbe. Since this gauge symmetry is spontaneously broken, an analogue of the Higgs mechanism must be present. We prove that a Heisenberg-like noncommutativity for the space coordinates is responsible for the breaking. This allows to interpret the noncommutativity of space coordinates as a Higgs mechanism on the quantum-mechanical U(1) gerbe

Agricultural Growth and Poverty Reduction: The Case of Mexico

Poverty levels have been diminishing in Mexico since the late 90's, although several regions still show high levels of poverty, and they are extremely high in some rural areas. This paper have addressed the issue of the linkages between sectoral growth (urban/rural) and poverty levels. It was found that although both types of growth impacted negatively on poverty levels in Mexico, rural growth seems to have a higher power in improving consumption per capita of the poorest among the poor people. Moreover, the only inter-sector linkage found was the one that connects rural growth with urban poverty for those people above the food -poverty line but below the moderate poverty line. Exploring plausible channels, we have found that rural growth enhances equality of income distribution at total and urban levels, while urban growth does exactly the opposite. But this is still a general equilibrium effect. Thus, we further explored labor market issues. We found that rural growth impacted positively on labor demand for unskilled worker: on this base, ceteris paribus it is better for poverty alleviation to have rural growth. We have also explored the issue of relative prices, although no impact of rural/urban growth was found here. Everything seems to be driven by the real exchange rate behavior. The share of agriculture in total income is relatively more important for poor people in rural areas, and most of the food poor people live in rural areas. This may be at the root of our findings.Food Security and Poverty, International Development, O18, O5, E2, J43,