An Infinitesimal Version of the Stone-von Neumann Theorem
Leonard Huang
TL;DR
This paper develops an infinitesimal formulation of the Stone-von Neumann Theorem, focusing on the uniqueness of the Heisenberg Commutation Relation using unbounded operators.
Contribution
It introduces an infinitesimal approach to the theorem, emphasizing the role of unbounded operators in the uniqueness property.
Findings
Infinitesimal version of the Stone-von Neumann Theorem established
Highlights the importance of unbounded operators in quantum mechanics
Provides a new perspective on the uniqueness of the Heisenberg relation
Abstract
In this paper, we present an infinitesimal version of the Stone-von Neumann Theorem. This work was motivated by the need to formulate the uniqueness property of the Heisenberg Commutation Relation purely in terms of unbounded operators.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Algebraic and Geometric Analysis · Matrix Theory and Algorithms