Geometric quantization: Particles, fields and strings

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

A Quantization Procedure of Fields Based on Geometric Langlands Correspondence

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group G. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundl...

Weyl Quantization from Geometric Quantization

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...

Fields, Strings and Branes

2 What is your aim in phylosophy? To show the fly the way out of the fly-bottle.

Nonlocal Particles as Strings

We find nonlocal particle theories with two dimensional conformal symmetry, including examples equivalent to the bosonic open string and closed string. This work provides a new approach to construct solvable consistent backgrounds in string theory.