Physics 495
Homework No. 11
1.
Solutions:
due Wednesday, 1 May, 2013
Remembering the denitions of the two dierent (complete sets of) single-particle states that
1
carry an irreducible representation of the Poincar group with mass m > 0 and spin s = 2 , na
Physics 495
Homework No. 10
1.
Solutions:
due Wednesday, 15 April, 2013
We know that the product of two boost matrices is not a boost, but rather a boost multiplied
by a rotation. The 4 4 matrix R(; n), usually referred to as the Wigner rotation, is dened
Physics 495
Homework No. 9
1.
due Monday, 1 April, 2013
Using our understanding of the worldlines of persons who accelerate at a constant value in their
own reference frame, please imagine that such a person is traveling from Earth to the nearest star,
C
Physics 495
Homework No. 8
1.
Solutions:
due Wednesday, 20 March, 2013
In a previous homework set, you were given the following equations that dene the transformation
between Cartesian and spherical basis sets.
dx = sin cos dr + r cos cos d r sin sin d ,
Physics 495
Homework No. 7
1.
Solutions:
due Wednesday, 6 March, 2013
The spherical harmonics of order = 1 are the following functions of spherical coordinates, where
we note those spherical coordinates as determined by the direction of a unit vector, tha
Physics 495
Homework No. 6
1.
Solutions:
due Wednesday, 27 February, 2013
Let the set of matrices cfw_M ()| SO(3, 1) be a representation of the Lorentz group. You will
recall that this means that when 3 = 1 2 then M (1 )M (2 ) = M (3 ). The mapping that
s
Physics 495
Homework No. 3
1.
Solutions:
due Wednesday, 6 February, 2013
Please consider the following diagram, which is a (labeled) x, t-diagram drawn by the standard
observer S , which is concerned with a single event, labeled R, which has t = 0 and x =
Physics 495
Homework No. 2
1.
Solutions:
due Wednesday, 30 January, 2013
We have discussed Hermiones trip to a distant star, 2 units away. We have seen Minkowski
diagrams showing her entire trip as measured by Arthur (resident on Earth) and also by Hermio
Physics 495
Homework No. 1
1.
due Wednesday, 23 January, 2013
The intent of this problem is that you should become (at least) somewhat familiar with the idea
of using units where c = 1. Therefore, please convert the following from natural units, i.e., wit