Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of Yang-Mills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the BRS/anti-BRS algebra is prese...

The notion of H-covariant strong Morita equivalence is introduced for ∗-algebras over C = R(i) with an ordered ring R which are equipped with a ∗-action of a Hopf ∗-algebra H . This defines a corresponding H-covariant strong Picard groupoid which encodes the entire Morita theory. Dropping the positivity conditions one obtains H-covariant ∗-Morita equivalence with its H-covariant ∗-Picard groupo...

We construct "soft-collinear gravity", the effective field theory which describes interaction of collinear and soft gravitons with matter (and themselves), to all orders in soft-collinear power expansion. Despite absence divergences gravity at leading power, construction exhibits remarkable similarities QCD (gauge fields). It reveals an emergent background gauge symmetry, allows for a manifestl...

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Co...

In this work we consider an efficient discretization of the Shallow Water Equations in spherical geometry for oceanographic applications. Instead classical 2d-covariant or 3d-Cartesian approaches, focus on mixed 3d/2d form Bernard et al. (2009) which evolves 2d momentum tangential to sphere by projecting right-hand side surface. Differently from last reference exact representation instead finit...

The class of the free relativistic covariant equations generated by the fractional powers of the D’Alambertian operator ( ) is studied. Meanwhile the equations corresponding to n = 1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n > 2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matr...

Recently, Sahlmann [1] proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a ⋆-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We ...

For a generic set in the Teichmüller space, we construct a covariant functor with the range in a category of the operator AF -algebras. The functor maps isomorphic Riemann surfaces to the stably isomorphic AF algebras. Our construction is based on a Hodge theory for measured foliations, elaborated by Hubbard, Masur and Thurston. As an application, we consider the following two problems: (i) a c...