318,079 research outputs found
Holomorphic Analogs of Topological Gauge Theories
We introduce a new class of gauge field theories in any complex dimension,
based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are
holomorphic analogs of the well-known Chern-Simons and BF topological theories
defined on real manifolds. We introduce actions for different special
holomorphic BF theories on complex, Kahler and Calabi-Yau manifolds and
describe their gauge symmetries. Candidate observables, topological invariants
and relations to integrable models are briefly discussed.Comment: 12 pages, LaTeX2e, shortened PLB versio
Character Varieties and the Moduli of Quiver Representations
Let G be a Lie group and Q a quiver with relations. In this paper, we define
G-valued representations of Q which directly generalize G-valued
representations of finitely generated groups. Although as G-spaces, the
G-valued quiver representations are more general than G-valued representations
of finitely generated groups, we show by collapsing arrows that their quotient
spaces are equivalent. We then establish a general criterion for the moduli of
G-valued quiver representations with relations to admit a strong deformation
retraction to a compact quotient by pinching vertices on the quiver. This
provides two different generalizations of main results in our previous work.
Lastly, we establish quiver theoretic conditions for the moduli spaces of
GL(n,C) and SL(n,C)-valued quiver representations to embed into traditional
moduli spaces of quiver representations having constant dimension vector.Comment: 37 pages; 5 figures; v3 has minor edits and added clarificatio
A tree approach to -variation and to integration
We consider a real-valued path; it is possible to associate a tree to this
path, and we explore the relations between the tree, the properties of
-variation of the path, and integration with respect to the path. In
particular, the fractal dimension of the tree is estimated from the variations
of the path, and Young integrals with respect to the path, as well as integrals
from the rough paths theory, are written as integrals on the tree. Examples
include some stochastic paths such as martingales, L\'evy processes and
fractional Brownian motions (for which an estimator of the Hurst parameter is
given)
Growth of Graded Twisted Calabi-Yau Algebras
We initiate a study of the growth and matrix-valued Hilbert series of
non-negatively graded twisted Calabi-Yau algebras that are homomorphic images
of path algebras of weighted quivers, generalizing techniques previously used
to investigate Artin-Schelter regular algebras and graded Calabi-Yau algebras.
Several results are proved without imposing any assumptions on the degrees of
generators or relations of the algebras. We give particular attention to
twisted Calabi-Yau algebras of dimension d at most 3, giving precise
descriptions of their matrix-valued Hilbert series and partial results
describing which underlying quivers yield algebras of finite GK-dimension. For
d = 2, we show that these are algebras with mesh relations. For d = 3, we show
that the resulting algebras are a kind of derivation-quotient algebra arising
from an element that is similar to a twisted superpotential.Comment: 49 page
One-sided division absolute valued algebras
We develop a structure theory for left division absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian dimension and with the additional property that they nave no nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation Relations" in Quantum Mechanics. We also show that homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive, hence automatically continuous
Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
Some years ago, Radzikowski has found a characterization of Hadamard states
for scalar quantum fields on a four-dimensional globally hyperbolic spacetime
in terms of a specific form of the wavefront set of their two-point functions
(termed `wavefront set spectrum condition'), thereby initiating a major
progress in the understanding of Hadamard states and the further development of
quantum field theory in curved spacetime. In the present work, we extend this
important result on the equivalence of the wavefront set spectrum condition
with the Hadamard condition from scalar fields to vector fields (sections in a
vector bundle) which are subject to a wave-equation and are quantized so as to
fulfill the covariant canonical commutation relations, or which obey a Dirac
equation and are quantized according to the covariant anti-commutation
relations, in any globally hyperbolic spacetime having dimension three or
higher. In proving this result, a gap which is present in the published proof
for the scalar field case will be removed. Moreover we determine the
short-distance scaling limits of Hadamard states for vector-bundle valued
fields, finding them to coincide with the corresponding flat-space, massless
vacuum states.Comment: latex2e, 41 page
On linear decompositions of L-valued simple graphs
In this report we will present a linear decomposition of a given L-
valued binary relation into a set of sub-relations of kernel-dimension one.
We will apply this theoretical result to the design of a faster algorithm for
computing L-valued kernels on general L-valued simple graphs
Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
In this paper, existence of generalized solutions to a thermodynamically
consistent Navier--Stokes--Cahn--Hilliard model introduced in [18] is proven in
any space dimension. The generalized solvability concepts are measure-valued
and dissipative solutions. The measure-valued formulation incorporates an
entropy inequality and an energy inequality instead of an energy balance in a
nowadays standard way, the Gradient flow of the internal variable is fulfilled
in a weak and the momentum balance in a measure-valued sense. In the
dissipative formulation, the distributional relations of the momentum balance
and the energy as well as entropy inequality are replaced by a relative energy
inequality. Additionally, we prove the weak-strong uniqueness of the proposed
solution concepts and that all generalized solutions with additional regularity
are indeed strong solutions
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