# Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory

@inproceedings{Moshayedi2020LecturesOS, title={Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theory}, author={Nima Moshayedi}, year={2020} }

These are lecture notes for the course “Poisson geometry and deformation quantization” given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we cover manifolds, tensor fields, integration on manifolds, Stokes’ theorem, de Rham’s theorem and Frobenius’ theorem. The second chapter covers the most important notions of symplectic geometry such as Lagrangian submanifolds, Weinstein’s tubular neighborhood…

## Figures from this paper

## References

SHOWING 1-10 OF 128 REFERENCES

### Relational symplectic groupoid quantization for constant poisson structures

- Computer Science
- 2016

The quantization constructed in this paper induces Kontsevich’s deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details and allows focussing on the BV-BFV technology and testing it.

### Shifted symplectic structures

- Mathematics
- 2011

This is the first of a series of papers about quantization in the context of derived algebraic geometry. In this first part, we introduce the notion of n-shifted symplectic structures (n-symplectic…

### Poisson geometry, deformation quantisation and group representations

- Mathematics
- 2005

Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an introduction…

### Shifted Poisson structures and deformation quantization

- Mathematics
- 2017

This paper is a sequel to ‘Shifted symplectic structures’ [T. Pantev, B. Toën, M. Vaquié and G. Vezzosi, Publ. Math. Inst. Hautes E'tudes Sci. 117 (2013) 271–328]. We develop a general and flexible…

### Lie-Poisson structure on some Poisson Lie groups

- Mathematics
- 1992

Poisson Lie groups appeared in the work of Drinfel'd (see, e.g., [Drl, Dr2]) as classical objects corresponding to quantum groups. Going in the other direction, we may say that a Poisson Lie group is…

### Momentum Maps and Morita Equivalence

- Mathematics
- 2003

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including the…

### Deformation Quantization of Poisson Manifolds

- Mathematics
- 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…

### A Path Integral Approach¶to the Kontsevich Quantization Formula

- Mathematics, Physics
- 1999

Abstract: We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path…

### Heat Kernels and Dirac Operators

- Mathematics
- 1992

The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent…