Wall crossing, discrete attractor flow and Borcherds algebra.
Ward identities from recursion formulas for correlation functions in conformal field theory
A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find -point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg and free...
Ward's solitons.
Wave Equation and Causality Violation
Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity
2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.
Wave operators for pairs of spaces and the Klein-Gordon equation.
Wave packets techniques
Weak c*-Hopf algebras: the coassociative symmetry of non-integral dimensions
By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C*-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplicative unitary of Baaj and Skandalis with a partial isometry. The algebraic properties, the existence of...
Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation
We consider an effective model of nuclear matter including spin and isospin degrees of freedom, described by an -body Hamiltonian with suitably renormalized two-body and three-body interaction potentials. We show that the corresponding mean-field theory (the time-dependent Hartree-Fock approximation) is “exact” as tends to infinity.
Weak Limits of Solutions to Semilinear Hyperbolic Sytems.
Wehrl entropy of the state in a two-atom Tavis-Cummings model
In this paper we present an entropic description of quantum state obtained by interaction of one mode of quantized electromagnetic field with two two-level atoms inside a cavity, known as Tavis-Cumming model. Wehrl entropy has been calculated analytically and investigated as a function of the average value of the photon number operator. Husimi's Q function has been calculated and compared with the behaviour of the field entropy.
Weyl algebra and a realization of the unitary symmetry
In the paper the origins of the intrinsic unitary symmetry encountered in the study of bosonic systems with finite degrees of freedom and its relations with the Weyl algebra (1979, Jacobson) generated by the quantum canonical commutation relations are presented. An analytical representation of the Weyl algebra formulated in terms of partial differential operators with polynomial coefficients is studied in detail. As a basic example, the symmetry properties of the -dimensional quantum harmonic oscillator...
Weyl manifold and quantized connection.
Weyl quantization for principal series.
Weyl quantization for the semidirect product of a compact Lie group and a vector space
Let be the semidirect product where is a semisimple compact connected Lie group acting linearly on a finite-dimensional real vector space . Let be a coadjoint orbit of associated by the Kirillov-Kostant method of orbits with a unitary irreducible representation of . We consider the case when the corresponding little group is the centralizer of a torus of . By dequantizing a suitable realization of on a Hilbert space of functions on where , we construct a symplectomorphism between...
Weyl sums and atomic energy oscillations.
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
What is the role of twistors in supergeometry.
When is a quantum space not a group?
We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as properties...
Why extended numbers in supersymmetry
Wigner distribution functions and the representation of canonical transformations in time-dependent quantum mechanics.