A category of quantum categories

Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature. We define notions of functor and natural transformation for quantum categories.Comment: Revised and expanded. A lot of diagrams. 40 page

Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-forms

We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini action of vielbein gravity formulated in terms of the solder form and spin connection, which are treated as independent variables. The basic geometrical constructions necessary for the DW Hamiltonian theory of vielbein gravity are presented. We reproduce the DW Hamilton equations in the multisymplectic and pre-multisymplectic formulations. We also give basic examples of Hamiltonian (n-1)-forms and related Poisson brackets.Comment: 47 pages, 0 figure v4 Minor corrections. (notations more light

Strong Coupling Running, Gauge Coupling Unification and the Scale of New Physics

The apparent unification of gauge couplings in Grand Unified Theories around 10$^{16}$ GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model. In this paper, an analysis of the measurements of the strong coupling running from the CMS experiment at the LHC is combined with a "traditional" gauge coupling unification analysis using data at the Z peak. This approach places powerful constraints on the possible scales of new physics and on the parameters around the unification scale. A supersymmetric analysis without GUT threshold corrections describes the CMS data well and provides perfect unification. The favored scales are $M_{SUSY}\ =\ 2820\ +670\ -540$GeV and$M_{GUT}\ =\ 1.05 \pm 0.06 \cdot 10^{16}$ GeV. For zero or small threshold corrections the scale of new physics may be well within LHC reach.Comment: 11 pages, 4 figures, 2 table