EuDML | Browse

Page 1

Displaying 1 – 9 of 9

Index and dynamics of quantized contact transformations

Steven Zelditch (1997)

Annales de l'institut Fourier

Quantized contact transformations are Toeplitz operators over a contact manifold $(X, α)$ of the form $U_{χ} = Π A χ Π$ , where $Π : H^{2} (X) \to L^{2} (X)$ is a Szegö projector, where $χ$ is a contact transformation and where $A$ is a pseudodifferential operator over $X$ . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine $ind (U_{χ})$ when the principal symbol is unitary, or equivalently to determine...

Integration and the Feynman-Kac formula

Igor Kluvánek (1987)

Studia Mathematica

Introduction aux méthodes euclidiennes en théorie quantique des champs

E. Combet (1985)

Publications du Département de mathématiques (Lyon)

Introduction to noncommutative differential geometry.

Omori, H. (1999)

Lobachevskii Journal of Mathematics

Invariant symbolic calculus for compact Lie groups

Benjamin Cahen (2019)

Archivum Mathematicum

We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.

Invariant symbolic calculus for semidirect products

Benjamin Cahen (2018)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be the semidirect product $V ⋊ K$ where $K$ is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space $V$ . Let $π$ be a unitary irreducible representation of $G$ which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of $G$ whose little group is a maximal compact subgroup of $K$ . We construct an invariant symbolic calculus for $π$ , under some technical hypothesis. We give some examples including the Poincaré group.

Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...

Itô calculus and quantisation of Lie bialgebras

R. L. Hudson (2005)

Annales de l'I.H.P. Probabilités et statistiques

Itô versus Woronowicz calculus in Itô Hopf algebras

Robin L. Hudson (2004)

Mathematica Slovaca

Displaying 1 – 9 of 9

Currently displaying 1 – 9 of 9