Search results for " Form"

Functional Derivative Approach

2001

Let us now leave the path integral formalism temporarily and reformulate operatorial quantum mechanics in a way which will make it easy later on to establish the formal connection between operator and path integral formalism. Our objective is to introduce the generating functional into quantum mechanics. Naturally we want to generate transition amplitudes. The problem confronting us is how to transcribe operator quantum mechanics as expressed in Heisenberg’s equation of motion into a theory formulated solely in terms of c-numbers. This can be achieved either by Schwinger’s action principle or with the aid of a generation functional defined as follows:

Star-products and phase space realizations of quantum groups

1992

It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.

Some seminorms on quasi*-algebras

2003

Dieren t types of seminorms on a quasi -algebra (A; A0) are constructed from a suitable family F of sesquilinear forms on A. Two particular classes, extended C -seminorms and CQ -seminorms, are studied in some detail. A necessary and sucien t condition for the admissibility of a sesquilinear form in terms of extended C -seminorms on (A; A0) is given.

Vectors, Tensors, Manifolds and Special Relativity

2015

Assuming that the reader is familiar with the notion of vectors, within a few pages, with a few examples, the reader will get to be familiar with the generic picture of tensors. With the specific notions given in this chapter, the reader will be able to understand more advanced tensor courses with no further effort. The transition between tensor algebra and tensor calculus is done naturally with a very familiar example. The notion of manifold and a few basic key aspects on Special Relativity are also presented.

Tsen–Lang Theory for Cpi-fields

1995

CY-Operators and L-Functions

2019

This a write up of a talk given at the MATRIX conference at Creswick in 2017 (to be precise, on Friday, January 20, 2017). It reports on work in progress with P. Candelas and X. de la Ossa. The aim of that work is to determine, under certain conditions, the local Euler factors of the L-functions of the fibres of a family of varieties without recourse to the equations of the varieties in question, but solely from the associated Picard–Fuchs equation.

Modular quintics inℙ4

2003

We will examine the arithmetic of some of the members of a pencil of symmetric quintics in projective 4-space. We will give evidence for the modularity of some of the exceptional members (even the non-rigid ones) and give a proof in one rigid case. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Current Algebras as Hilbert Space Operator Cocycles

1994

Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.

On the Estimation of the Volatility-Growth Link

2012

It is common practice to estimate the volatility-growth link by specifying a standard growth equation such that the variance of the error term appears as an explanatory variable in this growth equation. The variance in turn is modeled by a second equation. Hardly any of existing applications of this framework includes exogenous controls in this second variance equation. Our theoretical findings suggest that the absence of relevant explanatory variables in the variance equation leads to a biased and inconsistent estimate of the volatility-growth link. Our simulations show that this effect is large. Once the appropriate controls are included in the variance equation consistency is restored. I…

Regulation of IgE production and airway reactivity by CD4(-)CD8(-) regulatory T cells

2015

The mechanisms of tolerance induction occurring in the course of allergen-specific immunotherapy have not been elucidated in full detail. Our study aimed to characterize high zone tolerance in mouse models of type I allergy and of allergic airway inflammation induced by subcutaneous sensitization of mice with high doses of the model allergen ovalbumin (OVA) without the use of adjuvant. Mice were immunized by subcutaneous injection of high doses (HD) of OVA or, for comparison, low doses (LD) of OVA in saline. HD-mice showed lower specific IgE, but augmented IgG in sera than LD-mice. Pre-treatment of mice with HD-OVA antigen-specifically inhibited IgE production subsequently induced by LD-OVA…