Clavelli-Shapiro Trick

Computing the expected energy for a harmonic oscillator in a heat bath isn't bad. Other observables aren't too bad either, but here is a trick that will generalize.

First introduce new b operators obeying the same commutation relations.

To compute the thermal expectation value with parameter y ( fugacity goes with chemical potential, I mean the one that corresponds to temperature), you take the regular expectation value of your operator, but replace all the a's and their adjoints by

respectively.

3 Proofs in A.6 at least in a useful special case.

This seems insanely useful depending on how far it is pushed.

Relative QFT

http://arxiv.org/pdf/1212.1692.pdf

Expectation 5.3: Given a real Lie algebra, invariant inner product such that all coroots have length square 2, and a full lattice in the Cartan such that on the lattice the inner product is integral and even, there should exist a 7 dimensional topological quantum field theory and a 6 dimensional theory relative to it.

This is supposed to be the big goal of the (2,0) siX theory.

A relative QFT is an extended field theory in one higher dimension. To be continued...

Decay