Schwarz, Giacomo (2012) *Philosophical Aspects of Spontaneous Symmetry Breaking.* [Preprint]

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## Abstract

This essay expounds the algebraic framework describing general physical theories, within which the phenomenon of spontaneous symmetry breaking (SSB) makes its appearance in infinite quantum systems. This is in contrast with the fact that a large class of theories - both classical and quantum, finite and infinite - are termed, in the conventional account of classical and quantum mechanics, as exhibiting SSB. This discrepancy will be understood in the light of an interpretation that finds the symmetry breaking to be in some respects stronger in the algebraic account than is generally the case in the conventional picture.

The case of SSB in the standard account of quantum field theory (QFT) will then be discussed, and it will be argued that, although one would expect a connection with the algebraic account to be possible, this turns out to be problematic. Finally the role of the idealisation of infinite systems, crucial to algebraic SSB, will be discussed.

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Item Type: | Preprint |
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Additional Information: | This essay was submitted for the Masters level course, Part III, in the Department of Applied Mathematics and Theoretical Physics, Cambridge University, May 2012. |

Keywords: | Spontaneous symmetry breaking, c-star algebras, GNS theorem, infinite spin chain, algebraic quantum field theory, heuristic quantum field theory. |

Subjects: | Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories |

Depositing User: | Mr. Giacomo Schwarz |

Date Deposited: | 05 Sep 2012 16:07 |

Last Modified: | 05 Sep 2012 16:07 |

Item ID: | 9303 |

URI: | http://philsci-archive.pitt.edu/id/eprint/9303 |

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