Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories

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.Comment: Latex v2.09, 15 pages, to appear in Int. J. Mod. Phys.

Legendre expansion of the neutrino-antineutrino annihilation kernel: Influence of high order terms

We calculate the Legendre expansion of the rate of the process $\nu + \bar{\nu} \leftrightarrow e^+ + e^-$ up to 3rd order extending previous results of other authors which only consider the 0th and 1st order terms. Using different closure relations for the moment equations of the radiative transfer equation we discuss the physical implications of taking into account quadratic and cubic terms on the energy deposition outside the neutrinosphere in a simplified model. The main conclusion is that 2nd order is necessary in the semi-transparent region and gives good results if an appropriate closure relation is used.Comment: 14 pages, 4 figures. To be published in A&A Supplement Serie

Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phase-space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of General Relativity, or other generally covariant theories, only closes as a soft algebra and not a a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra --with structure constants-- but a soft algebra --with structure {\it functions}.Comment: 22 pages, version to be published in Classical & Quantum Gravit

BV analysis for covariant and non-covariant actions

The equivalence between the covariant and the non-covariant version of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of Electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the coratiant and non-covariant approaches, which had not been fully clarified in the literature.Comment: 21 pages, preprint # UTTG-02-93, UB-ECM-PF 93/5. To appear in Phys. Rev.

Faddeev-Jackiw approach to gauge theories and ineffective constraints

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.Comment: 21 pages, Latex. To be published in Int. J. Mod. Phys.