{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# PS7 - 253a/Schwartz Due Problem Set 7 1 Majorana...

This preview shows pages 1–2. Sign up to view the full content.

253a/Schwartz Due October 26, 2010 Problem Set 7 1. Majorana representation a) Write out the form of the Lorentz generators in the Majorana representation. b) Calculate γ 5 = 0 γ 1 γ 2 γ 3 in the Majorana representation. 2. In practice, we only rarely use explicit representations of the Dirac matrices. Most calcu- lations can be done using algebraic identities that depend only on { γ μ ν } = 2 η μν . Derive algebraically (without using an explicit representation): a) ( γ 5 ) 2 = 1 b) γ μ p γ μ = - 2 p c) γ μ p q p γ μ = ? d) { γ 5 μ } = ? e) Tr[ γ α γ μ γ β γ ν ] = 4( η αμ η βν - η αβ η μν + η αν η μβ ) 3. Show that s u s ( p ) u ¯ s ( p ) = p + m and s v s ( p ) v ¯ s ( p ) = p - m . 4. Derive the Gordon identity (with σ μν = i 2 [ γ μ ν ] ): u ¯( q ) γ μ u ( p ) = u ¯( q ) bracketleftbigg q μ + p μ 2 m + i σ μν ( q ν - p ν ) 2 m bracketrightbigg u ( p ) . (1) We will use this when we calculate the 1-loop correction the electron’s magnetic dipole moment. 5. Relativistic corrections to the Schrodinger equation.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

PS7 - 253a/Schwartz Due Problem Set 7 1 Majorana...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online