Secondary Calculus and the Covariant Phase Space

The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a fully rigorous approach to the covariant phase space in the framework of secondary calculus. In particular we describe the degeneracy distribution of w. As a byproduct we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.Comment: 40 pages, typos correcte

Electroabsorption spectroscopy of amorphous Si/SiC quantum well structures

Copyright 1989 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Applied Physics Letters, 55(8), 763-765, 1989 and may be found at http://dx.doi.org/10.1063/1.10179

On Triple Mutual Information

The mutual information of two random variables plays fundamental roles in many areas of applied mathematics. This quantity can be generalized to finite sets of random variables by (1). In contrast to the non-negativity of the usual mutual information, the triple mutual information can be negative as well as positive and its sign gives us a rough indication of the mode of mutual dependency among three random variables. The purpose of this note is to determine the range of the triple mutual information and to exarnin when the extremals are attained