ps06 - Physics 651 – Problem Set 6(due NO CLASS THE WEEK...

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Unformatted text preview: Physics 651 – Problem Set 6 (due 10/20/03) NO CLASS THE WEEK OF OCT 13. Read Chapter 3 to p. 52 (the classical part). 1. Show by explicit computation that the following Dirac (or spinor) representation ; J μν = S μν with S μν = i 4 [ γ μ , γ ν ], where γ ν are the Dirac matrices satisfying { γ μ , γ ν } = 2 g μν 1 , with 1 being the unit matrix, satisfies the Lorentz algebra : [ J μν , J ρσ ] = i ( g νρ J μσ- g μρ J νσ- g νσ J μρ + g μσ J νρ ) . 2. Do problem 3.1 3. a) Show explicitly that the Weyl (or chiral) representation of the Dirac matrices γ = 1 1 ! , γ i = σ i- σ i ! satisfies the Dirac algebra { γ μ , γ ν } = 2 g μν 1 . Show that the “standard” represen- tation γ = 1- 1 ! , γ i = σ i- σ i ! satisfies the same algebra. Write down γ 5 in each representation. b) Given a set of Dirac matrices γ μ , show that the matrices γ μ = S- 1 γ μ S with an arbitrary nonsingular matrix S also obey the Dirac algebra. Find the trans-also obey the Dirac algebra....
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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.

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ps06 - Physics 651 – Problem Set 6(due NO CLASS THE WEEK...

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