Symmetries
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Symmetries
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 University of Texas at Arlington
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 Phys 3446  Nuclear and Particle Physics
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PHYS 3446 Lecture 18 Wednesday Nov 8 2006 Dr Jae Yu 1 Symmetries Wednesday Nov 8 2006 Why do we care about the symmetry Symmetry in Lagrangian formalism Symmetries in quantum mechanical system Isospin symmetry Local gauge symmetry PHYS 3446 Fall 2006 Jae Yu 1 Announcements No lecture next Monday Nov 13 but SH105 is reserved for your discussions concerning the projects Quiz next Wednesday Nov 15 in class 2nd term exam Wednesday Nov 22 Covers Ch 4 whatever we finish on Nov 20 Reading assignments 10 3 and 10 4 Wednesday Nov 8 2006 PHYS 3446 Fall 2006 Jae Yu 2 Quantum Numbers We ve learned about various newly introduced quantum numbers as a patch work to explain experimental observations Lepton numbers Baryon numbers Isospin Strangeness Some of these numbers are conserved in certain situation but not in others Very frustrating indeed These are due to lack of quantitative description by an elegant theory Wednesday Nov 8 2006 PHYS 3446 Fall 2006 Jae Yu 3 Why symmetry Some quantum numbers are conserved in strong interactions but not in electromagnetic and weak interactions Inherent reflection of underlying forces Understanding conservation or violation of quantum numbers in certain situations is important for formulating quantitative theoretical framework Wednesday Nov 8 2006 PHYS 3446 Fall 2006 Jae Yu 4 Why symmetry When is a quantum number conserved When there is an underlying symmetry in the system When the quantum number is not affected or is conserved by under the changes in the physical system Noether s theorem theorem If there is a conserved quantity associated with a physical system there exists an underlying invariance or symmetry principle responsible for this conservation Symmetries provide critical restrictions in formulating theories Wednesday Nov 8 2006 PHYS 3446 Fall 2006 Jae Yu 5 Symmetries in Lagrangian Formalism Symmetry of a system is defined by any set of transformations that keep the equation of motion unchanged or invariant Equations of motion can be
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