Lecture.9.Local.Gauge.Invariance

Lecture.9.Local.Gauge.Invariance - LocalGaugeInvarianceand

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Local Gauge Invariance and Existence of the Gauge Particles 1. Gauge transformations are like “rotations” 2. How do functions transform under “rotations”? 3. How can we generalize to rotations in “strange” spaces ( spin space, , flavor space, color space )? 4. How are Lagrangians made invariant under these “rotations”? (Lagrangians “laws of physics” for particles interactions.) 5 . Invariance of L requires the existence of the gauge boson!
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omentum operator momentum operator x component omentum operator momentum operator
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angular momentum operator e ngular momentum operator generates rotations in y,z ace! The angular momentum operator , generates rotations in x,y,z space!
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One can generate the “rotation” of a spinor (like the u derived for the electron) using the “spin” operators: This approach is used in the Standard Model to “rotate” a particle which has an “up” and a “down” kind of property ‐‐ like flavor!
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Gauge transformations are like the
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Lecture.9.Local.Gauge.Invariance - LocalGaugeInvarianceand

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