Twisted calculus

Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

We construct an abstract pseudodifferential calculus with operatorvalued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the BornOppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a...

Twisted bundles and twisted K-theory

Many papers have been devoted recently to twisted K-theory as originally defined in [15] and [29]. See for instance the references [2], [23] and the very accessible paper [30]. We offer here a more direct approach based on the notion of “twisted vector bundles”. This is not an entirely new idea, since we find it in [4], [6], [7], [8] and [9] for instance, under different names and from various ...

Twisted Alexander Invariants of Twisted Links

Let L = 1∪· · ·∪ d+1 be an oriented link in S3, and let L(q) be the d-component link 1 ∪· · ·∪ d regarded in the homology 3-sphere that results from performing 1/q-surgery on d+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.

Twisted Radio Waves and Twisted Thermodynamics

We present and analyze a gedanken experiment and show that the assumption that an antenna operating at a single frequency can transmit more than two independent information channels to the far field violates the Second Law of Thermodynamics. Transmission of a large number of channels, each associated with an angular momenta 'twisted wave' mode, to the far field in free space is therefore not po...

Complex Interpolation and Twisted Twisted Hilbert Spaces