Download EBOOK The Philosophical Significance of Unitarily Inequivalent Representations in Quantum Field Theory PDF for free
 
Category: Society & Social Sciences
The author of the book: Tracy Alexander Lupher
Format files: PDF, EPUB, TXT, DOCX
The size of the: 918 KB
Language: English
ISBN13: 9781243525208
Edition: Proquest, Umi Dissertation Publishing
Date of issue: 3 September 2011

Description of the book "The Philosophical Significance of Unitarily Inequivalent Representations in Quantum Field Theory":
This dissertation gives a general account of the properties of unitarily inequivalent representations (UIRs) in both canonical quantum field theory and algebraic quantum field theory. A simple model is constructed and then used to show how to build a broad spectrum of UIRs including a version of Haag's theorem. Haag and Kastler, two of the founding fathers of algebraic quantum field theory, argue that the problems posed by UIRs are solved by adopting a notion of equivalence that is weaker than unitary equivalence, which they refer to as physical equivalence. In the dissertation, it is shown that their notion does not PDF provide a suitable classificatory schema. Some of the most important physical representations fail to satisfy the mathematical conditions of their notion. However, Haag and Kastler's notion has an unexpected connection with classical observables. A theorem is proven in which two representations make the same predictions with respect to all classical observables if and only if they satisfy their notion of physical equivalence. Following Haag and Kastler's lead, it was claimed by most proponents of algebraic quantum field theory that all physical content resides in a specific class of observables. It is shown in the dissertation ePub that such claims are exaggerated and misleading. UIRs are used to elucidate the nature of quantum field theory by showing that UIRs have different expectation values for some classical observables of the system, such as temperature and chemical potential, which are not in Haag and Kastler's specific class. It is shown how UIRs may be used to construct classical observables. To capture the physical content of quantum field theory it is shown that a much larger algebra than that of Haag and Kastler is necessary. Finally, the arguments that UIRs are incommensurable theories are shown to be flawed PDF. The lesson of UIRs is that the mathematical structures in both canonical quantum field theory and Haag and Kastler's version of algebraic quantum field theory are not sufficient to capture all of the physical content that UIRs represent. A suitable algebraic structure for quantum field theory is provided in the dissertation.
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Tracy Alexander Lupher
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