On Koopman-von Neumann Waves

In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently than what happens in quantum mechanics. The role of the phases associated to these classical "wave functions" is analyzed in details. In this framework we also perform the analog of the two-slit experiment and compare it with the quantum case.Comment: 27+1 pages, 2 figure

Quantization as a dimensional reduction phenomenon

Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well-known method of geometric quantization.Comment: 19 pages, Talk given by EG at the conference "On the Present Status of Quantum Mechanics", Mali Losinj, Croatia, September 2005. New results are contained in the last part of the pape

A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces

In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis and the Nijenhuis-Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.Comment: 27+1 pages, Latex, no figure

Near-infrared photometry of globular clusters towards the Galactic bulge: Observations and photometric metallicity indicators

Indexación: Web of Science; Scopus.We present wide-field JHKS photometry of 16 Galactic globular clusters located towards the Galactic bulge, calibrated on the Two Micron All-Sky Survey photometric system. Differential reddening corrections and statistical field star decontamination are employed for all of these clusters before fitting fiducial sequences to the cluster red giant branches (RGBs). Observed values and uncertainties are reported for several photometric features, including the magnitude of the RGB bump, tip, the horizontal branch (HB) and the slope of the upper RGB. The latest spectroscopically determined chemical abundances are used to build distance- and reddening-independent relations between observed photometric features and cluster metallicity, optimizing the sample size and metallicity baseline of these relations by supplementing our sample with results from the literature.We find that the magnitude difference between the HB and the RGB bump can be used to predict metallicities, in terms of both iron abundance [Fe/H] and global metallicity [M/H], with a precision of better than 0.1 dex in all three near-IR bandpasses for relatively metal-rich ([M/H] ≳ -1) clusters. Meanwhile, both the slope of the upper RGB and the magnitude difference between the RGB tip and bump are useful metallicity indicators over the entire sampled metallicity range (-2 ≲ [M/H] ≲ 0) with a precision of 0.2 dex or better, despite model predictions that the RGB slope may become unreliable at high (near-solar) metallicities. Our results agree with previous calibrations in light of the relevant uncertainties, and we discuss implications for clusters with controversial metallicities as well as directions for further investigation.https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stw243