563 research outputs found
Operads, configuration spaces and quantization
We review several well-known operads of compactified configuration spaces and
construct several new such operads, C, in the category of smooth manifolds with
corners whose complexes of fundamental chains give us (i) the 2-coloured operad
of A-infinity algebras and their homotopy morphisms, (ii) the 2-coloured operad
of L-infinity algebras and their homotopy morphisms, and (iii) the 4-coloured
operad of open-closed homotopy algebras and their homotopy morphisms. Two
gadgets - a (coloured) operad of Feynman graphs and a de Rham field theory on C
- are introduced and used to construct quantized representations of the
(fundamental) chain operad of C which are given by Feynman type sums over
graphs and depend on choices of propagators.Comment: 58 page
The extended moduli space of special Lagrangian submanifolds
It is well known that the moduli space of all deformations of a compact
special Lagrangian submanifold in a Calabi-Yau manifold within the
class of special Lagrangian submanifolds is isomorphic to the first de Rham
cohomology group of . Reinterpreting the embedding data within
the mathematical framework of the Batalin-Vilkovisky quantization, we find a
natural deformation problem which extends the above moduli space to the full de
Rham cohomology group of .Comment: 15pages. A new citation and a correctio
Deformation quantization of the -tuple point
Contrary to the classical methods of quantum mechanics, the deformation
quantization can be carried out on phase spaces which are not even topological
manifolds. In particular, the Moyal star product gives rise to a canonical
functor from the category of affine analytic spaces to the category of
associative (in general, non-commutative) \C-algebras. Curiously, if is
the -tuple point, , then is the algebra of
matrices.Comment: LaTeX, 7 page
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