Higher spins, quadratic forms and amplitudes

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Massless Higher Spins and Holography

We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R. The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consiste...

Quadratic Functions, Optimization, and Quadratic Forms

Linear-quadratic Control and Quadratic Differential Forms

We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...

Euclidean Quadratic Forms and Adc-forms: I

Introduction 2 1. Normed Rings 4 1.1. Elementwise Norms 4 1.2. Ideal norms 5 1.3. Finite Quotient Domains 5 1.4. Euclidean norms 6 2. Euclidean quadratic forms and ADC forms 7 2.1. Euclidean quadratic forms 7 2.2. Euclideanity 7 2.3. ADC-forms 8 2.4. Euclidean Forms are ADC Forms 8 2.5. The Generalized Cassels-Pfister Theorem 9 2.6. Maximal Lattices 10 3. Localization and Completion 11 3.1. Loc...