Angle theta (physical)

In Quantum physics, in the theory of measurement and according to the Hamiltonian formulation, the function of wave is function of the matter φ field and of the connection of measurement, noted A. a decomposition of the Espace of Hilbert can be carried out in sectors of supersélections characterized by their angle theta .

This theory imposes constraints of first class in the form of differential equations of functions, for example the Contrainte Gauss.

In a flat space time, space is a noncompressible whole of R ³. Since the constraints of Gauss are local, it is enough to consider the transformation U which approaches 1 when space tends towards the infinite one. Or then, one can consider that space is a S³ sphere. Under all the reports/ratios, one can see that there is a transformation U, homotopic with the transformation of measurement. These transformations are called small tranformations of measurement, in opposition to the others, called great transformations of measurement, classified in the group of homotopy π₃ (G) with G the group of measurement.

The constraint of Gauss under hears that the value of the function of wave is constant it on the orbit of the small transformation of measurement:

$\Psi=\Psi$

This relation is true for all the small transformations U, but not in a general way for all the great transformations.

It appears that if G is a Groupe of Dregs, π₃ (G) is Z , the whole of the relative numbers. If U represents a transformation of measurement from invariant topological 1, then the space of Hilbert breaks up into sectors of supersélection, marked by a angle theta θ such as:

$\ Psi=e^ {I \ theta} \ Psi$

Random links: