Generalized BRST Quantization and Massive Vector Fields

A previously proposed generalized BRST quantization on inner product spaces for second class constraints is further developed through applications. This BRST method involves a conserved generalized BRST charge Q which is not nilpotent but which satisfies Q=\delta+\delta^{\dagger}, \delta^2=0, and by means of which physical states are obtained from the projection \delta|ph>=\delta^{\dagger}|ph>=0. A simple model is analyzed in detail from which some basic properties and necessary ingredients are extracted. The method is then applied to a massive vector field. An effective theory is derived which is close to the one of the Stueckelberg model. However, since the scalar field here is introduced in order to have inner product solutions, a massive Yang-Mills theory with polynomial interaction terms might be possible to construct.Comment: 19 pages,Latexfil

On the entropy operator for the general SU(1,1) TFD formulation

In this letter, an entropy operator for the general unitary SU(1,1) TFD formulation is proposed and used to lead a bosonic system from zero to finite temperature. Namely, considering the closed bosonic string as the target system, the entropy operator is used to construct the thermal vacuum. The behaviour of such a state under the breve conjugation rules is analized and it was shown that the breve conjugation does not affect thermal effects. From this thermal vacuum the thermal energy, the entropy and the free energy of the closed bosonic string are calculated and the apropriated thermal distribution for the system is found after the free energy minimization.Comment: 13 pages, revtex4, minor typos corrected, references adde

Recent Developments in Enantioselective Transition Metal Catalysis Featuring Attractive Noncovalent Interactions between Ligand and Substrate.

Enantioselective transition metal catalysis is an area very much at the forefront of contemporary synthetic research. The development of processes that enable the efficient synthesis of enantiopure compounds is of unquestionable importance to chemists working within the many diverse fields of the central science. Traditional approaches to solving this challenge have typically relied on leveraging repulsive steric interactions between chiral ligands and substrates in order to raise the energy of one of the diastereomeric transition states over the other. By contrast, this Review examines an alternative tactic in which a set of attractive noncovalent interactions operating between transition metal ligands and substrates are used to control enantioselectivity. Examples where this creative approach has been successfully applied to render fundamental synthetic processes enantioselective are presented and discussed. In many of the cases examined, the ligand scaffold has been carefully designed to accommodate these attractive interactions, while in others, the importance of the critical interactions was only elucidated in subsequent computational and mechanistic studies. Through an exploration and discussion of recent reports encompassing a wide range of reaction classes, we hope to inspire synthetic chemists to continue to develop asymmetric transformations based on this powerful concept.The EPSRC are acknowledged in manuscript as they provide a studentship to one of the authors