2015arXiv (Cornell University)Open access

Classical Fermionic Dynamics

Luther Rinehart

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Abstract

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.

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The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.

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Available abstract

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.

Key concepts: Quantization (signal processing), Poisson bracket, Observable, Canonical quantization, Geometric quantization, Mathematics, Algebra over a field, Classical mechanics

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