151 research outputs found
Holomorphic deformation of Hopf algebras and applications to quantum groups
In this article we propose a new and so-called holomorphic deformation scheme
for locally convex algebras and Hopf algebras. Essentially we regard converging
power series expansion of a deformed product on a locally convex algebra, thus
giving the means to actually insert complex values for the deformation
parameter. Moreover we establish a topological duality theory for locally
convex Hopf algebras. Examples coming from the theory of quantum groups are
reconsidered within our holomorphic deformation scheme and topological duality
theory. It is shown that all the standard quantum groups comprise holomorphic
deformations. Furthermore we show that quantizing the function algebra of a
(Poisson) Lie group and quantizing its universal enveloping algebra are
topologically dual procedures indeed. Thus holomorphic deformation theory seems
to be the appropriate language in which to describe quantum groups as deformed
Lie groups or Lie algebras.Comment: 40 page
More transition amplitudes on the Riemann sphere
We consider a conformal field theory for bosons on the Riemann sphere.
Correlation functions are defined as singular limits of functional integrals.
The main result is that these amplitudes define transition amplitudes, that is
multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.Comment: 20 page
Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1)
The group Diff(S^1) of the orientation preserving diffeomorphisms of the
circle S^1 plays an important role in conformal field theory. We consider a
subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity".
This subgroup is of interest for the actual physical theory living on the
punctured circle, or the real line. We investigate the unique central extension
K of the Lie algebra of that group. We determine the first and second
cohomologies, its ideal structure and the automorphism group. We define a
generalization of Verma modules and determine when these representations are
irreducible. Its endomorphism semigroup is investigated and some unitary
representations of the group which do not extend to Diff(S^1) are constructed.Comment: 34 pages, no figur
The Boundaries of "Marketisation" - The Myth about Entrepreneurial Employees
Kühl S. The Boundaries of "Marketisation" - The Myth about Entrepreneurial Employees. In: Sachsenmeier P, Schottenloher M, eds. Challenges Between Competition and Collaboratio. The Future of the European Manufacturing Industry. Berlin, Heidelberg, New York: Springer; 2003: 231-252
Envelopes of holomorphy and extension of functions of bounded type
We study the extension of holomorphic functions of bounded type defined on an
open subset of a Banach space, to larger domains. For this, we first
characterize the envelope of holomorphy of a Riemann domain over a Banach
space, with respect to the algebra of bounded type holomorphic functions, in
terms of the spectrum of the algebra. We then give a simple description of the
envelopes of balanced open sets and relate the concepts of domain of holomorphy
and polynomial convexity. We show that for bounded balanced sets, extensions to
the envelope are always of bounded type, and that this does not necessarily
hold for unbounded sets, answering a question posed by Hirschowitz in 1972. We
also consider extensions to open subsets of the bidual, present some
Banach-Stone type results and show some properties of the spectrum when the
domain is the unit ball of .Comment: 25 page
Time Evolution of the External Field Problem in QED
We construct the time-evolution for the second quantized Dirac equation
subject to a smooth, compactly supported, time dependent electromagnetic
potential and identify the degrees of freedom involved. Earlier works on this
(e.g. Ruijsenaars) observed the Shale-Stinespring condition and showed that the
one-particle time-evolution can be lifted to Fock space if and only if the
external field had zero magnetic components. We scrutinize the idea, observed
earlier by Fierz and Scharf, that the time-evolution can be implemented between
time varying Fock spaces. In order to define these Fock spaces we are led to
consider classes of reference vacua and polarizations. We show that this
implementation is up to a phase independent of the chosen reference vacuum or
polarization and that all induced transition probabilities are well-defined and
unique.Comment: 60 pages, 1 figure, revised introduction, summary of results added,
typos correcte
Zero-one survival behavior of cyclically competing species
Coexistence of competing species is, due to unavoidable fluctuations, always
transient. In this Letter, we investigate the ultimate survival probabilities
characterizing different species in cyclic competition. We show that they often
obey a surprisingly simple, though non-trivial behavior. Within a model where
coexistence is neutrally stable, we demonstrate a robust zero-one law: When the
interactions between the three species are (generically) asymmetric, the
`weakest' species survives at a probability that tends to one for large
population sizes, while the other two are guaranteed to extinct. We rationalize
our findings from stochastic simulations by an analytic approach.Comment: 4 pages, 3 figure
Two formalisms, one renormalized stress-energy tensor
We explicitly compare the structure of the renormalized stress-energy tensor
(RSET) of a massless scalar field in a (1+1) curved spacetime as obtained by
two different strategies: normal-mode construction of the field operator and
one-loop effective action. We pay special attention to where and how it is
encoded the information related to the choice of vacuum state in both
formalisms. By establishing a clear translation map between both procedures, we
show that these two potentially different RSET are actually equal, when using
vacuum-state choices related by this map. One specific aim of the analysis is
to facilitate the comparison of results regarding semiclassical effects in
gravitational collapse as obtained within these different formalisms.Comment: 9 pages, no figures; v2: minor changes, version accepted for
publicatio
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