Related papers: Reflection Positivity---A Representation Theoretic…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we…
Phenomenological aspects of radiation by relativistic electrons in external field, in matter or the vicinity of matter are reviewed, among which: infrared divergence, coherence length effects, shadowing, enhancement in aligned crystals,…
This paper presents a photo elicitation project that invites students to explore their identities in STEM and surface the cultural wealth they bring into the physics classroom. Grounded in critical race theory, educational theory, and…
The evolution of RHEED reflexes intensity during reconstructed transitions characterizes (often implicitly) reconstructed surface state peculiarities. The approaches of a correct RHEED data interpretation, aimed at obtaining information…
In recent years, a change in attitude in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially…
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…
Using the integral representations of the solutions of Schr\"odinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the…
In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity,…
This is a survey of vanishing and positivity theorems for Hodge modules, and their recent applications to birational and complex geometry, expanding on my lecture at the 2015 AMS Summer Institute.
The importance of spatial non-locality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first…
A new method is presented, that can help a person become aware of his or her unconscious preferences, and convey them to others in the form of verbal explanation. The method combines the concepts of reflection, visualization, and…
The light-front dynamics is an efficient approach to study of field theory and of relativistic composite systems (nuclei at relativistic relative nucleon momenta, hadrons in the quark models). The explicitly covariant version of this…