Remarks on quantum mechanics on surfaces

We point out that the intrinsic second order Dirac theory on a surface in ordinary three-dimensional space exhibits a new scalar potential which is induced by the interaction between intrinsic spin and surface geometry. This term is absent in all scalar theories, including Schrödinger theory but also the Dirac theory in a surface based on the generic dimensional reduction framework of da Costa (1981) [1]. We relate, but do not restrict, the discussion to the physics of fullerens and point to some physical implications which might be used to discriminate between a description of the quantum physics on fullerens based on the intrinsic Dirac or the dimensionally reduced theory.