Heisenberg and Noncommutative Algebra

CLASSICAL MODEL: the algebra of observable physical quantities can ben directly read from the group G of emitted frequencies.

Since G is a commutative group, the convolution algebra is commutative.

In reality one is not dealing with a group of frequencies, but rather, due to the Ritz-Ridberg combination principle, with a groupoid:

D={(i,j) : i,j \in I}

having the composition rule

(i,j)*(j,k)=(i,k)

The convolution algebra of the groupoid D is none other than the algebra od matrices, since the convolution product may be written

(a,b)_i,k = \sum_i,j a(i,j)b(j,k)

which is identical to the product rule for matrices.

=> REPLACE THE COMMUTATIVE CONVOLUTION ALGEBRA OF THE GROUP G BY THE NON COMMUTATIVE CONVOLUTION ALGEBRA OF THE GROUPOID D.

source: Alain Connes, Non Commutative Geometry

live from Pisa

Le piccole cose (non necessariamente belle) che si imparano studiando meccanica quantistica.

A Göttingen c'è la tomba di Born con scolpito il valore di [p,q] (io non lo scrivo perchè non riesco a trovarlo sulla tastiera...)

A piccolo player must be right on pitch, whereas a double bass player can afford to wear garden gloves. For the piccolo a sixty-fourth note contains many full cycles, and the frequency is well defined, whereas for the bass, at a much lower register, the sixty-fourth note contains only a few cycles, and all you hear is the general sort of "oomph" with no very clear pitch. (D.J.Griffiths)

Grazie sig Griffiths per disprezzare noi poveri suonatori di strumenti grandi e dal suono grave... :(

setting boundary conditions..

Come nel caso del birapporto tempo fa, e della ruffineria ancora prima, in questo post mi servirò di concetti matematici per descrivere alcuni aspetti della mia esistenza..

..have fun guessing..

In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.