2 Path Integrals 3 2.1 Gaussian Integrals and Beyond... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Gauge-fixing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Gauge-fixing: Faddeev—Popov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Gauge-fixing: BRST . . . . . . . . . . . . . . . . . . . . . . ...

We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central extension of the constraint algebra, which can be “lifted”. Finally we write down the equations defining physical states and comment on their physical content....

Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the Heisenberg algebra over curved manifolds of non trivial topology involve topology classes of flat U(1) bundles. On the other hand, through some examples, the recently...

A classical action is proposed which upon quantisation yields massless particles belonging to the continuous spin representation of the Poincaré group. The string generalisation of the action is identical to the tensionless extrinsic curvature action proposed by Savvidy. We show that the BRST quantisation of the string action gives a critical dimension of 28. The constraints result in a number ...

Ternary filters have tap values limited to −1, 0, or +1. This restriction in tap values greatly simplifies the multipliers required by the filter, making ternary filters very well suited to hardware implementations. Because they incorporate coarse quantisation, their performance is typically limited by tap quantisation error. This paper derives formulae for estimating the achievable performance...