# Generalised Complex Geometry and the Planck Cone

@article{Isidro2004GeneralisedCG, title={Generalised Complex Geometry and the Planck Cone}, author={Jos{\'e} Maria Isidro}, journal={arXiv: High Energy Physics - Theory}, year={2004} }

Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a complex structure on classical phase space. In this letter we analyse the role played by generalised complex geometry in the classical and quantum mechanics of a finite number of…

## 3 Citations

### Abelian gerbes as a gauge theory of quantum mechanics on phase space

- Physics
- 2006

We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space . The connection is given by a triple of forms A, B, H: a potential 1-form A, a Neveu–Schwarz potential…

### DIRAC BRACKETS FROM MAGNETIC BACKGROUNDS

- Physics
- 2007

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalized complex…

### STAR PRODUCTS ON GENERALIZED COMPLEX MANIFOLDS

- Mathematics
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We regard classical phase space as a generalized complex manifold and analyze the B-transformation properties of the ⋆-product of functions. The C⋆-algebra of smooth functions transforms in the…

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