General Gauge Independence of Diamagnetism plus Paramagnetism

Strong Diamagnetism for General Domains and Applications

We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let B be the strength of the magnetic field, and let λ1(B) be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that B 7→ λ1(B) is monotone increasing for large B. Combined with the results of [FoHe2], this implies that all the ‘third’ critical fields for strongly Type II superco...

Atomic/Molecular Origin and Physics Description of Magnetic Susceptibility: Diamagnetism, Paramagnetism, Ferromagnetism, Superparamagnetism

 is negative in diamagnetic materials and positive in paramagnetic materials. This means that the field and NMR frequency are both typically reduced in diamagnetic materials and enhanced in paramagnetic materials (though in calculating it is important to take account of the effect of the sample shape and the sphere of Lorentz). Paramagnetic/diamagnetic materials are attracted/repelled by a m...

Strong diamagnetism for general domains and application

— We consider the Neumann Laplacian with constant magnetic field on a regular domain in R2. Let B be the strength of the magnetic field and let λ1(B) be the first eigenvalue of this Laplacian. It is proved that B 7→ λ1(B) is monotone increasing for large B. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 supercon...

Gauge invariance, gauge-parameter independence and properties of Green functions

The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying ...

General Gauge and Conditional Gauge