Implications of Conformal Invariance for Quantum Field Theories in d>2d>2

Recently obtained results for two and three point functions for quasi-primary operators in conformally invariant theories in arbitrary dimensions {\absit d} are described. As a consequence the three point function for the energy momentum tensor has three linearly independent forms for general {\absit d} compatible with conformal invariance. The corresponding coefficients may be regarded as possible generalisations of the Virasoro central charge to {\absit d} larger than 2. Ward identities which link two linear combinations of the coefficients to terms appearing in the energy momentum tensor trace anomaly on curved space are discussed. The requirement of positivity for expectation values of the energy density is also shown to lead to positivity conditions which are simple for a particular choice of the three coefficients. Renormalisation group like equations which express the constraints of broken conformal invariance for quantum field theories away from critical points are postulated and applied to two point functions.\hfill\break Talk presented at the XXVII Ahrenshoop International Symposium.Comment: 14pages, Damtp 93/6

Constraints on RG Flow for Four Dimensional Quantum Field Theories

The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve $a$, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric $G$ on the space of couplings and give rise to gradient flow like equations for $a$, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings $e^{2\sigma}$ to a form which involves running couplings $g_\sigma$ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa $\beta$-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric $G$ for this theory are also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when $\beta \to B$, a modified $\beta$-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa $\beta$-function. ${\cal N}=1$ supersymmetric Wess-Zumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.Comment: 86 pages, version 2, various corrections, section 3 significantly revised, version 3 further minor corrections, as to be published, version 4, some corrections and additional material in sections 2,

Liquid-hydrogen rocket engine development at Aerojet, 1944 - 1950

This program demonstrated the feasibility of virtually all the components in present-day, high-energy, liquid-rocket engines. Transpiration and film-cooled thrust chambers were successfully operated. The first liquid-hydrogen tests of the coaxial injector was conducted and the first pump to successfully produce high pressures in pumping liquid hydrogen was tested. A 1,000-lb-thrust gaseous propellant and a 3,000-lb-thrust liquid-propellant thrust chamber were operated satisfactorily. Also, the first tests were conducted to evaluate the effects of jet overexpansion and separation on performance of rocket thrust chambers with hydrogen-oxygen propellants