Lecture7.Guage.Invariance.Conserved.Quantities

Lecture7.Guage.Invariance.Conserved.Quantities - auge...

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Unformatted text preview: auge Invariance and Gauge Invariance and Conserved Quantities Noether's theorem was proven by German mathematician, Emmy Noether in 1915 and ublished 918 oether's eorem as ecome published in 1918. Noether s theorem has become a fundamental tool of quantum field theory and has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics". Amalie Emmy Noether 1882-1935 Consider the charged scalar field, and the following transformation on , where is a constant. =1 Now suppose that can be varied continuously so that we have an infinite number of small, continuous for which exp(i ) = and L L. The set of all these transformations, U = exp(i ), form a group of operators. It is called U(1) , a unitary group (because U * U = 1 ) Here the Hermitian conjugate is the complex conjugate because U is not a matrix. Now, we have a more astounding result: we can vary the (complex) phase...
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Lecture7.Guage.Invariance.Conserved.Quantities - auge...

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