Algebraic field theory on curved manifolds

Quantization on Curved Manifolds

Since the early days of quantum mechanics many techniques have been developed in order to deal with manifolds with non-trivial topology. Among them two techniques have received a great attention in the literature and are shortly reviewed here as they are most geometrical in nature. These are the Kostant–Souriau geometric quantization scheme and the so called constrained quantum mechanics. A not...

Quantum Field Theory on Curved Backgrounds

Quantum Field Theories on Manifolds with Curved Boundaries: Scalar Fields

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the Green function for second order differential operators valid in the neighbourhood of the boundary and which is obtained from a corresponding expansion of of the associated heat kernel derived earlier for arbitr...

Algebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds

Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...

Nonminimal Operator on Curved Manifolds

Asymptotic heat kernel expansion for nonminimal differential operators on curved manifolds in the presence of gauge fields is considered. The complete expressions for the fourth coefficient (E4) in the heat kernel expansion for such operators are presented for the first time. The expressions were computed for general case of manifolds of arbitrary dimension n and also for the most important cas...