# Diff anomaly

1. Sep 26, 2006

There is place one where it does not arise: QFT.

The Virasoro extension is a diff anomaly, defined in any dimension, and the analogous Kac-Moody-like extension is a gauge anomaly, proportional to the second Casimir. However, diff and gauge anomalies in QFT were classified many years ago; there are no diff anomalies in 4D, and gauge anomalies are proportional to the third Casimir. Hence these extensions can not arise in QFT proper.

However, they do arise in a minor modification of QFT, QJT (J for jet). To build the representations, all fields have to be replaced by their Taylor series. In doing so, a new datum is introduced: the expansion point (or rather curve). This is an important modification, because the relevant cocycles depend on it. The physical interpretation is that one must explictly consider the observer's trajectory in spacetime together with the quantum fields.

In view of this lesson from representation theory, I have been working on a reformulation of physics in terms of Taylor data. What is available from 2004, http://www.arxiv.org/abs/hep-th/0411028 , is still seriously flawed, although there was considerable progress compared to what I wrote in 1999, and a better version will be completed early next year. So it is not a new model, but rather a somewhat different framework for quantization.

There is easy to see that if you consider the Laurent polynomial version of the gauge algebra, anomalies are necessary for nonzero charge, cf. http://www.arxiv.org/abs/math-ph/0603024 . It does not really matter whether you consider diffeomorphisms, Yang-Mills or conformal transformations - the important difference is between Laurent and ordinary polynomials, or compact support. In particular, there is no conformal anomaly for polynomials, i.e. L_m with m >= -1.

Since I believe that Laurent polynomial gauge transformations should not be outlawed, and I certainly believe in nonzero charge, it follows that the new gauge anomalies exist and QFT must be replaced QJT.