a1014 - (1 point). 3. Calculate T A T S . Due April 19 in...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 14 (April 8, 2010) (51) An electron and a positron, each with mass equal to 0 . 511 MeV , annihilate at rest into two photons. Chose the rest frame of the positronium, such that one of the photons moves in positive x = x 1 direction. 1. For each photon ±nd the momentum 4-vector. 2. Find the 4-momentum in a frame that moves at a velocity ˆ x with respect to the rest frame of the positronium. 3. Suppose that the annihilation took place 10 9 years ago in a galaxy that is receding from us at β = 4 / 5. What is the energy of the photon that we observe? Due April 21 before class (10 points). (52) Let T αβ be a rank two tensor. 1. Write down T αβ S , the symmetric part of T αβ . Due April 19 in class (1 point). 2. Write down T αβ A , the antisymmetric part of T αβ . Due April 19 in class
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (1 point). 3. Calculate T A T S . Due April 19 in class (1 point). 4. Derive the continuity equation from the antisymmetry of F . Due April 19 in class (1 point). 5. Show * F = 0, where * F = 1 2 F is the dual tensor. Here is the completely antisymmetric Levi-Cevita tensors: +1 for ( , , , ) and even permutation of (0 , 1 , 2 , 3),-1 for ( , , , ) and even permutation of (0 , 1 , 2 , 3). Due April 19 in class (2 points). (53) Under a gauge transformation the vector potential transform according to A A = A + . Calculate the corresponding transformation of the electromagnetic eld tensor F F . Due April 21 before class (4 points)....
View Full Document

This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.

Ask a homework question - tutors are online