Symplectic Field Theory of the Galilean Covariant Scalar and Spinor Representations

We explore the concept of the extended Galilei group, a representation for the symplectic quantum mechanics in the manifold G, written in the light-cone of a five-dimensional de Sitter space-time in the phase space. The Hilbert space is constructed endowed with a symplectic structure. We study the unitary operators describing rotations and translations, whose generators satisfy the Lie algebra of G. This representation gives rise to the Schr¨odinger (Klein–Gordon-like) equation for the wave function in the phase space such that the dependent variables have the position and linear momentum contents. The wave functions are associated to the Wigner function through the Moyal product such that the wave functions represent a quasiamplitude of probability. We construct the Pauli–Schr¨odinger (Dirac-like) equation in the phase space in its explicitly covariant form. Finally, we show the equivalence between the five-dimensional formalism of the phase space with the usual formalism, proposing a solution that recovers the non-covariant form of the Pauli–Schr¨odinger equation in the phase space.

BOSON SEA VERSUS DIRAC SEA: GENERAL FORMULATION OF THE BOSON SEA THROUGH SUPERSYMMETRY

We consider the long standing problem in field theories of bosons that the boson vacuum does not consist of a "sea," unlike the fermion vacuum. We show with the help of supersymmetry considerations that the boson vacuum indeed does also consist of a sea in which the negative energy states are all "filled," analogous to the Dirac sea of the fermion vacuum, and that a hole produced by the annihilation of one negative energy boson is an antiparticle. Here, we must admit that it is only possible if we allow — as occurs in the usual formalism anyway — that the "Hilbert space" for the single particle bosons is not positive definite. This might be formally coped with by introducing the notion of a double harmonic oscillator, which is obtained by extending the condition imposed on the wave function. This double harmonic oscillator includes not only positive energy states but also negative energy states. We utilize this method to construct a general formalism for a boson sea analogous to the Dirac sea, irrespective of the existence of supersymmetry. The physical result is consistent with that of the ordinary second quantization formalism. We finally suggest applications of our method to the string theories.

On the Emergence of the Microcanonical Description from a Pure State

We study, in general terms, the process by which a pure state can "self-thermalize" and appear to be described by a microcanonical density matrix. This requires a quantum mechanical version of the Gibbsian coarse graining that conceptually underlies classical statistical mechanics. We make use of some extra degrees of freedom that are necessary for this. Interaction between these degrees and the system can be understood as a process of resonant absorption and emission of "soft quanta." This intuitive picture allows one to state a criterion for when self thermalization occurs. This paradigm also provides a method for calculating the thermalization rate using the usual formalism of atomic physics for calculating decay rates. We contrast our prescription for coarse graining, which is somewhat dynamical, with the earlier approaches that are intrinsically kinematical. An important motivation for this study is the black hole information paradox.

Catalytic effect of cetyltrimethylammonium bromide on the radical destruction oxidation of pyrocatechol violet

The effect of cetyltrimethylammonium bromide (I) on the radical oxidation of pyrocatechol violet by hydrogen peroxide was studied in the presence of N,N'-ethylenediamine-bis(o-aminobenzaldimine)cobalt(II) bromide and cobalt dichloride. After a short, faster period the reaction obeys the 1st order formalism. In the presence of I the experimental rate constants are as much as 42 times higher than in "pure" solutions. In optimum conditions (dye concentration 1.75 . 10-4 mol l-1) the reaction can be described in terms of the usual formalism of micellar catalysis. In solutions containing I the effect of cobalt compounds can be traced down to cobalt concentration levels of 10-8 mol l-1. The dependences of the experimental rate constants on the concentrations of hydrogen peroxide and cobalt compounds and on the temperature and pH are discussed.

Polar structures in the theory of conjugated molecules. II. Symmetry properties and matrix elements for polar structures

The inclusion of polar structures in the valence-bond theory of π-electrons entails some additions to the usual formalism, and these are given in this part. The symmetry properties of sets of structures, both non-polar and polar, and the matrix elements that come into energy calculations, are dealt with. Using the work of part I, and the conclusions of this part, the energy parameters for work with polar structures are evaluated.