University of Oxford Logo University of OxfordDepartment of Computer Science - Home
On Facebook
Facebook
Follow us on twitter
Twitter
Linked in
Linked in
Flickr
Flickr
Google plus
Google plus
Digg
Digg
Pinterest
Pinterest
Stumble Upon
Stumble Upon

Oxford Quantum Talks Archive

Graph models of the Heisenberg-Weyl algebra

Pawel Blasiak, Polish Academy of Sciences Krakow, University Paris-Nord
Categories, Logic and Foundations of Physics VI, March 2010, University of Oxford

The Heisenberg-Weyl algebra, underlying most physical realizations of Quantum Theory, is considered from a combinatorial point of view. We construct a concrete model of the algebra in terms of graphs which endowed with intuitive concepts of composition and decomposition provide a rich bi-algebra structure. It will be shown how this encompass the Heisenberg-Weyl algebra, thereby providing a straightforward interpretation of the latter as a shadow of natural constructions on graphs. In this way, by focusing on algebraic structure of Quantum Theory we intend to draw attention to genuine combinatorial underpinning of its formalism. We will also discuss some combinatorial methods suitable for this graphical calculus.

[video] [streaming video] [slides]