The equivalence between the Dirac method and Faddeev-Jackiw analysis for gauge theories is proved. In particular we trace out, in a stage by stage procedure, the standard classification of first and second class constraints of Dirac's method in the F-J approach. We also find that the Darboux transformation implied in the F-J reduction process can be viewed as a canonical transformation in Dirac approach. Unlike Dirac's method the F-J analysis is a classical reduction procedure, then the quantization can be achieved only in the framework of reduce and then quantize approach with all the know problems that this type of procedures presents. Finally we illustrate the equivalence by means of a particular example.UB-ECM-PF 95/15 hep-th/9610067

Tea is a widely consumed drink in the world which is susceptible to undergoing adulterations to reduce manufacturing costs and rise financial benefits. The development of simple analytical methodologies to assess tea authenticity, as well as to detect and quantify frauds, is an important matter considering the rise of adulteration issues in recent years. In the present study, untargeted HPLC-UV and HPLC-FLD fingerprinting methods were employed to characterize, classify, and authenticate tea extracts belonging to different varieties (red, green, black, oolong, and white teas) by partial least squares-discriminant analysis (PLS-DA), as well as to detect and quantify adulteration frauds when chicory was used as the adulterant by partial least squares (PLS) regression, to ensure the authenticity and integrity of foodstuffs. Overall, PLS-DA showed a good classification and grouping of the tea samples according to the tea variety and, except for some white tea extracts, perfectly discriminated from the chicory ones. One hundred percent classification rates for the PLS-DA calibration models were achieved, except for green and oolong tea when HPLC-FLD fingerprints were employed, which showed classification rates of 96.43% and 95.45%, respectively. Good predictions were also accomplished, also showing, in almost all the cases, a 100% classification rate for prediction, with the exception of white tea and oolong tea when HPLC-UV fingerprints were employed that exhibited a classification rate of 77.78% and 88.89%, respectively. Good PLS results for chicory adulteration detection and quantitation were also accomplished, with calibration, cross-validation, and external validation errors beneath 1.4%, 6.4%, and 3.7%, respectively. Acceptable prediction errors (below 21.7%) were also observed, except for white tea extracts that showed higher errors which were attributed to the low sample variability available.

The general conditions for the applicability of the Faddeev-Jackiw approach to gauge theories are studied. When the constraints are effective a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev-Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that the Dirac Hamiltonian can be enlarged to an Extended Hamiltonian including all first class constraints, without changes in the dynamics) and we suggest that when the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the correct dynamics. Finally we present some examples that illustrate this inequivalence.UB-ECM-PF 97/20 hep-th/9803222

It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we report the results in 1 showing that the same continues to hold true for pure Lovelock gravity of arbitrary order N for topology S (n) × S (n) . Thermodynamical stability of black hole discerns between odd and even N , and consequently between negative and positive Λ and it favors the former while rejecting the latter.