Search results for "Operator theory"

Hermitian natural differential operators

1986

Composite operators in asymptotic safety

2017

We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dim…

Considerations on super Poincare algebras and their extensions to simple superalgebras

2001

We consider simple superalgebras which are a supersymmetric extension of $\fspin(s,t)$ in the cases where the number of odd generators does not exceed 64. All of them contain a super Poincar\'e algebra as a contraction and another as a subalgebra. Because of the contraction property, some of these algebras can be interpreted as de Sitter or anti de Sitter superalgebras. However, the number of odd generators present in the contraction is not always minimal due to the different splitting properties of the spinor representations under a subalgebra. We consider the general case, with arbitrary dimension and signature, and examine in detail particular examples with physical implications in dimen…

Central extensions of the families of quasi-unitary Lie algebras

1998

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families …

The origin of in-plane stresses in axially moving orthotropic continua

2016

In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in th…

A new method for computing one-loop integrals

1994

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point functions both algebraically and numerically to all tensor cases. This program is written as a package for Maple. An additional Mathematica version is planned later.

Cohomology and contraction: The “non-relativistic” limit revisited

1984

In this note we reconsider the transition from P⊗U(1) to the N extended Galilei group \(\tilde G\)(m),first discussed by Saletan. To this aim, we first analyse the relations between the groups G⊗U(1) and \(\tilde G\)c , where G is a Lie group of trivial H o 2 (G,U(1)) cohomology and \(\tilde G\)c is a central extension of Gc (obtained from G by contraction) by U(1).

Failure of topological rigidity results for the measure contraction property

2014

We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.

The perturbation classes problem for closed operators

2017

We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.

Mapping properties for the Bargmann transform on modulation spaces

2010

We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.