Spectral Derivatives in C*-algebras
These are parts of a working paper on
The concept of spectral derivative is derived from
the idea of the of a quantum mechanical momentum
operator algebraically defined by the Canonical Commutation
Relations and represented
in the Schödinger representation as a derivative.
In the quantum mechanical case,
the derivative is taken, of functions defined on the
spectrum of the position operator with respect to the
variable that ranges over that spectrum.
In FCCR, presented in the physics pages,
the idea that physically suitable Canonical Commutation Relations
can be given in terms of nxn complex matricies that connect the
Canonical Commutation Relations (CCR) for n unbounded with the
Canonical Anticommutation Relations (CAR) for n=2.
A Spectral Derivative is supposed to adapt the formal
recipe for a derivative to the case of finite dimensional spaces,
and therefore to discrete operator spectra.
Return to Home Page
The URL for the page:
Email me, Bill Hammel at
READ WARNING BEFORE SENDING E-MAIL