3,370 research outputs found
Global algebras of nonlinear generalized functions with applications in general relativity
We give an overview of the development of algebras of generalized functions
in the sense of Colombeau and recent advances concerning diffeomorphism
invariant global algebras of generalized functions and tensor fields. We
furthermore provide a survey on possible applications in general relativity in
light of the limitations of distribution theory
On realization of generalized effect algebras
A well known fact is that there is a finite orthomodular lattice with an
order determining set of states which is not representable in the standard
quantum logic, the lattice of all closed subspaces of a
separable complex Hilbert space.
We show that a generalized effect algebra is representable in the operator
generalized effect algebra of effects of a
complex Hilbert space iff it has an order determining set of
generalized states.
This extends the corresponding results for effect algebras of Rie\v{c}anov\'a
and Zajac. Further, any operator generalized effect algebra possesses an order determining set of generalized states
The homotopy invariance of the string topology loop product and string bracket
Let M be a closed, oriented, n -manifold, and LM its free loop space.
Chas and Sullivan defined a commutative algebra structure in the homology of
LM, and a Lie algebra structure in its equivariant homology. These structures
are known as the string topology loop product and string bracket, respectively.
In this paper we prove that these structures are homotopy invariants in the
following sense.
Let f : M_1 \to M_2 be a homotopy equivalence of closed, oriented n
-manifolds. Then the induced equivalence, Lf : LM_1 \to LM_2 induces a ring
isomorphism in homology, and an isomorphism of Lie algebras in equivariant
homology. The analogous statement also holds true for any generalized homology
theory h_* that supports an orientation of the M_i 's.Comment: 21 pages, 2 figures final version published in Journal of Topolog
Asymmetric Cosets
The aim of this work is to present a general theory of coset models G/H in
which different left and right actions of H on G are gauged. Our main results
include a formula for their modular invariant partition function, the
construction of a large set of boundary states and a general description of the
corresponding brane geometries. The paper concludes with some explicit
applications to the base of the conifold and to the time-dependent Nappi-Witten
background.Comment: 34 pages, LaTeX, 8 figures, 1 table, v2: references added, v3: typos
correcte
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