Star products on graded manifolds and $\alpha '$-corrections to Courant algebroids from string theory

Understand

Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately.

• If the algebra being deformed is that of observables, the result is deformation quantization, independent of any realization in terms of Hilbert space operators.
• There are very important but rare cases in which a formula for a full deformation is known.
• For physics, the most important is the Moyal-Weyl star product formula.