Geometric topology and connections with quantum field theory.
... of K(X) as families of Fredholm operators parametrized by X) is still missing. This is despite a two decade old proposal of Graeme Segal to interpret elements of the elliptic cohomology of X essentially as families of conformal field theories parametrized by X. Segal gave the opening lecture in the ...
... of K(X) as families of Fredholm operators parametrized by X) is still missing. This is despite a two decade old proposal of Graeme Segal to interpret elements of the elliptic cohomology of X essentially as families of conformal field theories parametrized by X. Segal gave the opening lecture in the ...
QUANTUM CHAOS DOMINIQUE DELANDE Laboratoire Kastler-Brossel
... sensitivity on initial conditions, hence cannot be chaotic in the ordinary sense! However, the previous statement must be considered with care. Indeed, classical mechanics can also be seen as a linear theory if one considers the evolution of a classical phase space density ρ(q, p, t) given by the Li ...
... sensitivity on initial conditions, hence cannot be chaotic in the ordinary sense! However, the previous statement must be considered with care. Indeed, classical mechanics can also be seen as a linear theory if one considers the evolution of a classical phase space density ρ(q, p, t) given by the Li ...
Department of Physics, Chemistry and Biology Master’s Thesis Four-component DFT calculations of
... is the electronic wave function Φelec . This wave function depends explicitly on the electronic coordinates, but parametrically on the nuclear coordinates, as does the electronic energy. So the total energy for fixed nuclei must also include the repulsion term between nuclei Etot = Eelec + Vnn ...
... is the electronic wave function Φelec . This wave function depends explicitly on the electronic coordinates, but parametrically on the nuclear coordinates, as does the electronic energy. So the total energy for fixed nuclei must also include the repulsion term between nuclei Etot = Eelec + Vnn ...
Angular momentum of the photon
... 3.Measurement of the photon spin Experimental proof of that theoretical prediction was done by R. Beth in 1936 in Princeton. As Beth announces in his paper (R. A. Beth, Mechanical Detection and Measurement of the Angular Momentum of Light, Physical Review, v. 50, July 15, 1936) he had several discu ...
... 3.Measurement of the photon spin Experimental proof of that theoretical prediction was done by R. Beth in 1936 in Princeton. As Beth announces in his paper (R. A. Beth, Mechanical Detection and Measurement of the Angular Momentum of Light, Physical Review, v. 50, July 15, 1936) he had several discu ...
Broken symmetry revisited - Homepages of UvA/FNWI staff
... (gauge) symmetry. The signature of a broken continuous global symmetry group G in a physical system is the occurrence of massless scalar degrees of freedom, the so-called Goldstone bosons. Specifically, each broken generator of G gives rise to a massless Goldstone boson field. Well-known realization ...
... (gauge) symmetry. The signature of a broken continuous global symmetry group G in a physical system is the occurrence of massless scalar degrees of freedom, the so-called Goldstone bosons. Specifically, each broken generator of G gives rise to a massless Goldstone boson field. Well-known realization ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.