arXiv subjects
Publications and source records attributed to T Porter.
We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NG_n\cap D_n where D_n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.
The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg-Zilber theory from Tonks' thesis, and of its relation to simplicial homotopy coherence. Again, our results give information not just on the homotopy classification of certain equivariant maps, but also on the weak equivariant homotopy type of the corresponding equivariant function spaces.
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.