Theoretical Physics

4 December 2013
Time: 15:00 to 16:00
Location: EC Stoner SR 8.60

Stefan Weigert (York)

Triples of Pairwise Canonical Observables

Given a quantum particle on a line, its momentum and
position are described by a pair of Hermitean operators
(p, q) which satisfy the canonical commutation relation
(CCR). A third observable r exists which satisfies CCRs
with both position and momentum. The triple (p, q, r) is not
only unique (up to unitary equivalence) but also maximal
in the sense that no four equi-commutant observables
exist. Being invariant under cyclic permutations, the
triple (p, q, r) endows the Heisenberg algebra with a
threefold, largely unexplored symmetry.

I will discuss consequences of the equi-commutant triple
(p,q,r) and its exponentiated cousin, called a Weyl triple.
For example, a generalisation of Heisenberg's uncertainty
relation involving three standard deviations is proposed,
and the non-trivial minimizing state can be found (joint
work with S Kechrimparis). The triples are also relevant
for a general theory of mutually unbiased bases.



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