7,283 research outputs found
Structural Aspects of Two-Dimensional Anomalous Gauge Theories
A foundational investigation of the basic structural properties of
two-dimensional anomalous gauge theories is performed. The Hilbert space is
constructed as the representation of the intrinsic local field algebra
generated by the fundamental set of field operators whose Wightman functions
define the model. We examine the effect of the use of a redundant field algebra
in deriving basic properties of the models and show that different results may
arise, as regards the physical properties of the generalized chiral model, in
restricting or not the Hilbert space as representation of the intrinsic local
field algebra. The question referring to considering the vector Schwinger model
as a limit of the generalized anomalous model is also discussed. We show that
this limit can only be consistently defined for a field subalgebra of the
generalized model.Comment: 40 pages. Latex, to appear in Annals of Physic
Symmetries and Paraparticles as a Motivation for Structuralism
This paper develops an analogy proposed by Stachel between general relativity
(GR) and quantum mechanics (QM) as regards permutation invariance. Our main
idea is to overcome Pooley's criticism of the analogy by appeal to
paraparticles.
In GR the equations are (the solution space is) invariant under
diffeomorphisms permuting spacetime points. Similarly, in QM the equations are
invariant under particle permutations. Stachel argued that this feature--a
theory's `not caring which point, or particle, is which'--supported a
structuralist ontology.
Pooley criticizes this analogy: in QM the (anti-)symmetrization of fermions
and bosons implies that each individual state (solution) is fixed by each
permutation, while in GR a diffeomorphism yields in general a distinct, albeit
isomorphic, solution.
We define various versions of structuralism, and go on to formulate Stachel's
and Pooley's positions, admittedly in our own terms. We then reply to Pooley.
Though he is right about fermions and bosons, QM equally allows more general
types of symmetry, in which states (vectors, rays or density operators) are not
fixed by all permutations (called `paraparticle states'). Thus Stachel's
analogy is revived.Comment: 45 pages, Latex, 3 Figures; forthcoming in British Journal for the
Philosophy of Scienc
Geometry of invariant domains in complex semi-simple Lie groups
We investigate the joint action of two real forms of a semi-simple complex
Lie group S by left and right multiplication. After analyzing the orbit
structure, we study the CR structure of closed orbits. The main results are an
explicit formula of the Levi form of closed orbits and the determination of the
Levi cone of generic orbits. Finally, we apply these results to prove
q-completeness of certain invariant domains in S.Comment: 20 page
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