2,267 research outputs found
Monopole fields from vortex sheets reconciling Abelian and center dominance
We describe a new order parameter for the confinement-deconfinement
transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of
magnetic monopole field correlators represented as sums over sheets of center
vortices. Our construction establishes a link between "abelian" and "center
dominance". It avoids an inconsistency in the treatment of small scales present
in earlier definitions of monopole fields by respecting Dirac's quantization
condition for magnetic fluxes.Comment: LaTeX file, 6 pages; Lattice2001(plenary
Supersymmetric quantum theory and (non-commutative) differential geometry
We reconsider differential geometry from the point of view of the quantum
theory of non-relativistic spinning particles, which provides examples of
supersymmetric quantum mechanics. This enables us to encode geometrical
structure in algebraic data consisting of an algebra of functions on a manifold
and a family of supersymmetry generators represented on a Hilbert space. We
show that known types of differential geometry can be classified in terms of
the supersymmetries they exhibit. Replacing commutative algebras of functions
by non-commutative *-algebras of operators, while retaining supersymmetry, we
arrive at a formulation of non-commutative geometry encompassing and extending
Connes' original approach. We explore different types of non-commutative
geometry and introduce notions of non-commutative manifolds and non-commutative
phase spaces. One of the main motivations underlying our work is to construct
mathematical tools for novel formulations of quantum gravity, in particular for
the investigation of superstring vacua.Comment: 125 pages, Plain TeX fil
Asymptotic Completeness for Compton Scattering
Scattering in a model of a massive quantum-mechanical particle, an
``electron'', interacting with massless, relativistic bosons, ``photons'', is
studied. The interaction term in the Hamiltonian of our model describes
emission and absorption of ``photons'' by the ``electron''; but
``electron-positron'' pair production is suppressed. An ultraviolet cutoff and
an (arbitrarily small, but fixed) infrared cutoff are imposed on the
interaction term. In a range of energies where the propagation speed of the
dressed ``electron'' is strictly smaller than the speed of light, unitarity of
the scattering matrix is proven, provided the coupling constant is small
enough; (asymptotic completeness of Compton scattering). The proof combines a
construction of dressed one--electron states with propagation estimates for the
``electron'' and the ``photons''.Comment: gap of previous version closed, large parts rewritten, more general
results and more comprehensive exposition. 64 pages, 3 figure
Supersymmetric quantum theory and non-commutative geometry
Classical differential geometry can be encoded in spectral data, such as
Connes' spectral triples, involving supersymmetry algebras. In this paper, we
formulate non-commutative geometry in terms of supersymmetric spectral data.
This leads to generalizations of Connes' non-commutative spin geometry
encompassing non-commutative Riemannian, symplectic, complex-Hermitian and
(Hyper-)Kaehler geometry. A general framework for non-commutative geometry is
developed from the point of view of supersymmetry and illustrated in terms of
examples. In particular, the non-commutative torus and the non-commutative
3-sphere are studied in some detail.Comment: 77 pages, PlainTeX, no figures; present paper is a significantly
extended version of the second half of hep-th/9612205. Assumptions in Sect.
2.2.5 clarified; final version to appear in Commun.Math.Phy
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