Quantisation of second class systems in the Batalin-Tyutin formalism

We review the Batalin-Tyutin approach of quantising second class systems which consists in enlarging the phase space to convert such systems into first class. The quantisation of first class systems, it may be mentioned, is already well founded. We show how the usual analysis of Batalin-Tyutin may be generalised, particularly if one is dealing with nonabelian theories. In order to gain a deeper insight into the formalism we have considered two specific examples of second class theories-- the massive Maxwell theory (Proca model) and its nonabelian extension. The first class constraints and the involutive Hamiltonian are explicitly constructed. The connection of our Hamiltonian approach with the usual Lagrangian formalism is elucidated. For the Proca model we reveal the importance of a boundary term which plays a significant role in establishing an exact identification of the extra fields in the Batalin-Tyutin approach with the St\"uckelberg scalar. Some comments are also made concerning the corresponding identification in the nonabelian example.Comment: 26 pages, Latex file, e-mail [email protected] SINP-TNP/94-

Generalised Hamiltonian embedding of the Proca model

We convert the second class Proca model into a first class theory by using the generalised prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge invariant fields in the embedded model can be identified with the fundamental fields in the proca model as well as with the observables in the St\"uckelberg model or in the model involving the interaction of an abelian 2-form field with the Maxwell field. The connection of these models with the massive Kalb-Ramond model is also elucidated within a path integral approach.Comment: 11 pages, Latex, No figur

Spherical collapse with heat flow and without horizon

We present a class of solutions for a heat conducting fluid sphere, which radiates energy during collapse without the appearance of horizon at the boundary at any stage of the collapse. A simple model shows that there is no accumulation of energy due to collapse since it radiates out at the same rate as it is being generated.Comment: RevTeX, 3 page

Batalin-Tyutin Quantisation of the CPN−1CP^{N-1} model

The $CP^{N-1}$ model is quantised in the generalised canonical formalism of Batalin and Tyutin by converting the original second class system into first class. Operator ordering ambiguities present in the conventional quantisation scheme of Dirac are thereby avoided. The first class constraints, the involutive Hamiltonian and the BRST charge are explicitly computed. The partition function is defined and evaluated in the unitary gauge.Comment: 14 pages, SINP-TNP/93-1

Non abelian bosonisation in three dimensional field theory

We develop a method based on the generalised St\"uckelberg prescription for discussing bosonisation in the low energy regime of the SU(2) massive Thirring model in 2+1 dimensions. For arbitrary values of the coupling parameter the bosonised theory is found to be a nonabelian gauge theory whose physical sector is explicitly obtained. In the case of vanishing coupling this gauge theory can be identified with the SU(2) Yang-Mills Chern-Simons theory in the limit when the Yang-Mills term vanishes. Bosonisation identities for the fermionic current are derived.Comment: Latex version, 14 pages; 23 reference

Progression of endothelial dysfunction, atherosclerosis, and arterial stiffness in stable kidney transplant patients: a pilot study.

BACKGROUND: Kidney transplant patients suffer from vascular abnormalities and high cardiovascular event rates, despite initial improvements post-transplantation. The nature of the progression of vascular abnormalities in the longer term is unknown. This pilot study investigated changes in vascular abnormalities over time in stable kidney transplant patients long after transplantation. METHODS: Brachial artery flow-mediated dilation (FMD), nitroglycerin-mediated dilation, carotid-femoral pulse wave velocity (cf-PWV), ankle-brachial pressure index, and common carotid artery intima-media thickness (CCA-IMT) were assessed in 18 kidney transplant patients and 17 controls at baseline and 3-6 months after. RESULTS: There was no difference in age (51 ± 13 vs. 46 ± 11; P = 0.19), body mass index (26 ± 5 vs. 25 ± 3; P = 0.49), serum cholesterol (4.54 ± 0.96 vs. 5.14 ± 1.13; P = 0.10), systolic blood pressure (BP) (132 ± 12 vs. 126 ± 12; P = 0.13), diastolic BP (82 ± 9 vs. 77 ± 8; P = 0.10), or diabetes status (3 vs. 0; P = 0.08) between transplant patients and controls. No difference existed in vascular markers between patients and controls at baseline. In transplant patients, FMD decreased (- 1.52 ± 2.74; P = 0.03), cf-PWV increased (0.62 ± 1.06; P = 0.03), and CCA-IMT increased (0.35 ± 0.53; P = 0.02). No changes were observed in controls. CONCLUSION: Markers of vascular structure and function worsen in the post-transplant period on long-term follow-up, which may explain the continued high cardiovascular event rates in this population