# Koopman‐von Neumann formulation of classical Yang‐Mills theories: I

@article{Carta2006KoopmanvonNF, title={Koopman‐von Neumann formulation of classical Yang‐Mills theories: I}, author={Paolo Carta and Ennio Gozzi and D. Mauro}, journal={Annalen der Physik}, year={2006}, volume={15} }

In this paper we present the Koopman‐von Neumann (KvN) formulation of classical non‐Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang‐Mills theories concepts like gauge‐fixing and Faddeev‐Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang‐Mills theories. We…

## 8 Citations

### Koopman‐von Neumann formulation of classical Yang‐Mills theories: I

- PhysicsAnnalen der Physik
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## References

SHOWING 1-10 OF 66 REFERENCES

### Koopman‐von Neumann formulation of classical Yang‐Mills theories: I

- PhysicsAnnalen der Physik
- 2006

In this paper we present the Koopman‐von Neumann (KvN) formulation of classical non‐Abelian gauge field theories. In particular we shall explore the functional (or classical path integral)…

### Minimal Coupling in Koopman–von Neumann Theory

- Physics
- 2002

Abstract Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 1930s. They basically formalized, via…

### CHIRAL ANOMALIES VIA CLASSICAL AND QUANTUM FUNCTIONAL METHODS

- Mathematics
- 2005

In the quantum path integral formulation of a field theory model an anomaly arises when the functional measure is not invariant under a symmetry transformation of the Lagrangian. In this paper,…

### Hidden BRS invariance in classical mechanics. II.

- MathematicsPhysical review. D, Particles and fields
- 1989

An interpretation for the ghost fields as being the well-known Jacobi fields of classical mechanics is provided, and the Hamiltonian {ital {tilde H}}, derived from the action {ital{tilde S}}, turns out to be the Lie derivative associated with theHamiltonian flow.

### Hilbert space structure in classical mechanics. I

- Mathematics
- 2003

In this paper we study the Hilbert space structure underlying the Koopman–von Neumann (KvN) operatorial formulation of classical mechanics. KvN limited themselves to study the Hilbert space of…

### Renormalization of the abelian Higgs-Kibble model

- Physics
- 1975

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov…

### On the ``Universal'' N=2 Supersymmetry of Classical Mechanics

- Mathematics
- 2001

In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular, we try to shed some light on a N = 2 "universal"…