Unformatted text preview: out your calculation by integrating every other x ( t ). For example, for N = 8, ﬁrst you integrate x 1 , x 3 , x 5 and x 7 , resulting in a new N = 4. Next, you integrate x 2 and x 6 , resulting in a new N = 2. Finally you integrate x 4 to obtain the ﬁnal result. 3. Now generalize the path integral to the 3dim case. Rederive the Schroedinger equation from the path integral formalism for the 3dim case. 4. Show that the Lorentz generators L μν = i ( x μ ∂ νx ν ∂ μ ) form the Lie algebra of the Lorentz group. (That is, each of their commutators can be expressed as a linear combinations of L μν only.) Now include the translation generators P μ =i∂ μ . Show that, together, they form the Lie algebra of the Poincare group. Restrcting μ to spatial indices only, show that J i = ± ijk L jk / 2 form the usual angular momentum algebra. That is, the rotation group is a subgroup of the Lorentz group. 1...
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This note was uploaded on 09/28/2008 for the course PHYS 651 taught by Professor Tye,henry during the Fall '03 term at Cornell.
 Fall '03
 TYE,HENRY
 Physics, Quantum Field Theory

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