Local Physical Coodinates from Symplectic Projector Method

The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed.Comment: 8 page

Entropic Law of Force, Emergent Gravity and the Uncertainty Principle

The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completly classical is missleading. In this paper we argue that the entropic formulation provides new insights into the quantum nature of the inertia and the gravity. We use the entropic postulate to determine the quantum uncertainty in the law of inertia and in the law of gravity in the Newtonian Mechanics, the Special Relativity and in the General Relativity. These results are obtained by considering the most general quantum property of the matter represented by the Uncertainty Principle and by postulating an expression for the uncertainty of the entropy such that: i) it is the simplest quantum generalization of the postulate of the variation of the entropy and ii) it reduces to the variation of the entropy in the absence of the uncertainty.Comment: 10 pages. Important discussion of the special relativistic case and the newtonian limit of the general relativistic case added. The paper has been reformatted. The authorship listing corrected. (It has been published by mistake out of order in the first version. We have been adhering to the Hardy-Littlewood Rule over the years.) Typos corrected. Four references adde

Optical-NIR analysis of globular clusters in the IKN dwarf spheroidal: a complex star formation history

Age, metallicity and spatial distribution of globular clusters (GCs) provide a powerful tool to reconstruct major star-formation episodes in galaxies. IKN is a faint dwarf spheroidal (dSph) in the M81 group of galaxies. It contains five old GCs, which makes it the galaxy with the highest known specific frequency (SN=126). We estimate the photometric age, metallicity and spatial distribution of the poorly studied IKN GCs. We search SDSS for GC candidates beyond the HST field of view, which covers half of IKN. To break the age-metallicity degeneracy in the V-I colour we use WHT/LIRIS Ks-band photometry and derive photometric ages and metallicities by comparison with SSP models in the V,I,Ks colour space. IKN GCs' VIKs colours are consistent with old ages ($\geq\!8$ Gyr) and a metallicity distribution with a higher mean than typical for such a dSph ([Fe/H$]\!\simeq\!-1.4_{-0.2}^{+0.6}$ dex). Their photometric masses range ($0.5 <{\cal M_{\rm GC}}<4\times10^5M_\odot$) implies a high mass ratio between GCs and field stars, of $10.6\%$. Mixture model analysis of the RGB field stars' metallicity suggests that 72\% of the stars may have formed together with the GCs. Using the most massive GC-SFR relation we calculate a SFR of $\sim\!10M_\odot/$yr during its formation epoch. We note that the more massive GCs are closer to the galaxy photometric centre. IKN GCs also appear spatially aligned along a line close to the IKN major-axis and nearly orthogonal to the plane of spatial distribution of galaxies in the M81 group. We identify one new IKN GC candidate based on colour and PSF analysis of the SDSS data. The evidence towards i) broad and high metallicity distribution of the field IKN RGB stars and its GCs, ii) high fraction and iii), spatial alignment of IKN GCs, supports a scenario for tidally triggered complex IKN's SFH in the context of interactions with galaxies in the M81 group.Comment: 12 pages, 9 figures, accepted to A&

A tale of two Bethe ans\"atze

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ans\"atze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.Comment: 28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor changes to match the published versio