We investigate the interplay between the universal differential calculus and other known algebraic structures, like Hochschild boundary on one side, and the C* structure on the other.
The latter provides natural norms one can evaluate on forms; we will discuss a relevant application in the case of the algebra of Quantum Spacetime, that will be discussed and physically motivated.
One finds that, while the algebra itself is fully translation and Lorentz invariant, the four dimensional Euclidean distance is a positive operator bounded below by a constant of order one (in Planck units); the area operator and the four volume operator are normal operators, the latter being a Lorentz invariant operator with pure point spectrum, whose moduli are also bounded below by a constant of order one, whilst the spectrum of the 3 volume operator includes zero.
These findings are in perfect agreement with the physical intuition suggested by the Spacetime Uncertainty Relations which are implemented by the algebra of Quantum Spacetime.
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Last updated 30 April 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).