Algebraic Quantum Field Theory
Hans Halvorson,Michael Mueger +1 more
- Iss: 9780444515605, pp 731-864
TLDR
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools as mentioned in this paper.Abstract:
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.read more
Citations
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Between classical and quantum
TL;DR: In this article, the authors discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), and through decoherence and consistent histories.
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Connes' embedding problem and Tsirelson's problem
Marius Junge,Miguel Navascués,Carlos Palazuelos,David Pérez-García,Volkher B. Scholz,Reinhard F. Werner +5 more
TL;DR: In this article, Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras are essentially equivalent.
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Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
Tzyh Haur Yang,Miguel Navascués +1 more
TL;DR: In this article, it was shown that one can self-test a black box into any pure entangled two-qubit state by performing simple Bell-type experiments, using only one family of Bell inequalities with two inputs and two outputs.
Journal ArticleDOI
Connes' embedding problem and Tsirelson's problem
Marius Junge,Miguel Navascués,Carlos Palazuelos,David Pérez-García,Volkher B. Scholz,Reinhard F. Werner +5 more
TL;DR: In this paper, Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras are essentially equivalent.
Posted Content
Perturbative Algebraic Quantum Field Theory and the Renormalization Groups
TL;DR: In this paper, a new formalism for the perturbative construction of algebraic quantum field theory is developed, which allows the treatment of low dimensional theories and of non-polynomial interactions.
References
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Journal ArticleDOI
Phd by thesis
TL;DR: In this paper, a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) is presented.
Book
Fundamentals of the Theory of Operator Algebras
TL;DR: In this article, the authors compare normal states and unitary equivalence of von Neumann algebras, including the trace and the trace trace of the trace of a projection.
Journal ArticleDOI
On Unitary Representations of the Inhomogeneous Lorentz Group
TL;DR: The superposition principle of the wave function is defined in this article, which is the fundamental principle of quantum mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined.