Effects of nonlocality in time of interactions of an atom with its surroundings on the broadening of spectral lines of atoms

We investigate effects of nonlocality in time of the interaction of an atom with its surroundings on the spectral line broadening. We show that these effects can be very significant: In some cases nonlocality in time of this interaction can give rise to a spectral line splitting.Comment: 15 pages, 4 figures, to be published in Physics Letters

Symplectic fermions and a quasi-Hopf algebra structure on Uˉisl(2)\bar{U}_i sl(2)

We consider the (finite-dimensional) small quantum group $\bar{U}_q sl(2)$ at $q=i$. We show that $\bar{U}_i sl(2)$ does not allow for an R-matrix, even though $U \otimes V \cong V \otimes U$ holds for all finite-dimensional representations $U,V$ of $\bar{U}_i sl(2)$. We then give an explicit coassociator $\Phi$ and an R-matrix $R$ such that $\bar{U}_i sl(2)$ becomes a quasi-triangular quasi-Hopf algebra. Our construction is motivated by the two-dimensional chiral conformal field theory of symplectic fermions with central charge $c=-2$. There, a braided monoidal category, $\mathcal{SF}$, has been computed from the factorisation and monodromy properties of conformal blocks, and we prove that $\mathrm{Rep}\,(\bar{U}_i sl(2),\Phi,R)$ is braided monoidally equivalent to $\mathcal{SF}$.Comment: 40pp, 11 figures; v2: few very minor corrections for the final version in Journal of Algebr

Fusion and braiding in finite and affine Temperley-Lieb categories

Finite Temperley-Lieb (TL) algebras are diagram-algebra quotients of (the group algebra of) the famous Artin's braid group $B_N$, while the affine TL algebras arise as diagram algebras from a generalized version of the braid group. We study asymptotic `$N\to\infty$' representation theory of these quotients (parametrized by $q\in\mathbb{C}^{\times}$) from a perspective of braided monoidal categories. Using certain idempotent subalgebras in the finite and affine algebras, we construct infinite `arc' towers of the diagram algebras and the corresponding direct system of representation categories, with terms labeled by $N\in\mathbb{N}$. The corresponding direct-limit category is our main object of studies. For the case of the finite TL algebras, we prove that the direct-limit category is abelian and highest-weight at any $q$ and endowed with braided monoidal structure. The most interesting result is when $q$ is a root of unity where the representation theory is non-semisimple. The resulting braided monoidal categories we obtain at different roots of unity are new and interestingly they are not rigid. We observe then a fundamental relation of these categories to a certain representation category of the Virasoro algebra and give a conjecture on the existence of a braided monoidal equivalence between the categories. This should have powerful applications to the study of the `continuum' limit of critical statistical mechanics systems based on the TL algebra. We also introduce a novel class of embeddings for the affine Temperley-Lieb algebras and related new concept of fusion or bilinear $\mathbb{N}$-graded tensor product of modules for these algebras. We prove that the fusion rules are stable with the index $N$ of the tower and prove that the corresponding direct-limit category is endowed with an associative tensor product. We also study the braiding properties of this affine TL fusion.Comment: 50p

Nonlocality of nucleon interaction and an anomalous off shell behavior of the two-nucleon amplitudes

The problem of the ultraviolet divergences that arise in describing the nucleon dynamics at low energies is considered. By using the example of an exactly solvable model it is shown that after renormalization the interaction generating nucleon dynamics is nonlocal in time. Effects of such nonlocality on low-energy nucleon dynamics are investigated. It is shown that nonlocality in time of nucleon-nucleon interactions gives rise to an anomalous off-shell behavior of the two-nucleon amplitudes that have significant effects on the dynamics of many-nucleon systems.Comment: 9 pages, 4 figures, ReVTeX