Scholarlink

This manuscript is based on a series of lectures given in the XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering. While quantum mechanics is widely presented within the Hilbert space formalism in undergraduate courses, in these notes we give an introduction to its algebraic formulation. It is based on the theory of \(C^{*}\) -algebras, which is shortly outlined here. This viewpoint is more general than the usual formulation of quantum mechanics, because of the the non-uniqueness of irreducible representations of \(C^{*}\) -algebras of infinite dimension. This is related to the Rosenberg theorem and Naimark’s problem.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

\(C^{*}\) -Algebraic Formulation of Quantum Mechanics

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • J.-B. Bru,
  • W. de Siqueira Pedra

摘要

This manuscript is based on a series of lectures given in the XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering. While quantum mechanics is widely presented within the Hilbert space formalism in undergraduate courses, in these notes we give an introduction to its algebraic formulation. It is based on the theory of \(C^{*}\) -algebras, which is shortly outlined here. This viewpoint is more general than the usual formulation of quantum mechanics, because of the the non-uniqueness of irreducible representations of \(C^{*}\) -algebras of infinite dimension. This is related to the Rosenberg theorem and Naimark’s problem.