Physics 610
1
Homework 4 Solutions
Asymptotic series
Consider the baby or toy version of scalar 4 theory, where it is just a single integral;
2 4
+
2
24
Z=
d exp
.
(1)
This is what the path integral f
Physics 610, Problem Set 2
due: Friday, September 23 at 3:30pm
Please place your completed problem sets in the Physics 610 box in the physics department
mailroom (Rutherford 103b) before the due date.
Physics 610, Problem Set 3
due: Friday, September 30 at 3:30pm
Please place your completed problem sets in the Physics 610 box in the physics department mailroom
(Rutherford 103b) before the due date.
Physics 610, Problem Set 1
due: Friday, September 16 at 3:30pm
Please place your completed problem sets in the Physics 610 box in the physics department
mailroom (Rutherford 103b) before the due date.
Physics 610, Problem Set 4
due: Friday, October 14 at 3:30pm
Please place your completed problem sets in the Physics 610 box in the physics department mailroom
(Rutherford 103b) before the due date. P
Physics 610
1
Homework 10 solutions
Renormalization
Consider scalar 4 theory, with one real scalar eld and Lagrangian
m2 2 0 4
1
.
(1)
L =
2
2
24
We have seen many times that the lowest-order matrix
Physics 610
1
Homework 7 Solutions
Spinors
In class we found explicit expressions for the spinors up,s and vp,s for the special case that
1
p = (E, 0, 0, pz ) (E 2 = p2 + m2 as usual) and s = 2 along
Physics 610
1
Homework 8 Solutions
Complete Set of Grassmann States
For i , i , i , i each independent n-member sets of Grassmann variables, and using the
summation convention i i i i i , prove the id
Physics 610
1
Homework 9 Solutions
Spinor-Scalar Scattering in Yukawa Theory
Consider Yukawa theory, with one Dirac fermion and one real scalar eld , with Lagrangian
M2 2
1
/
4 (y i 5 y ) .
(1)
L = (
Physics 610
1
Homework 6 solutions
Fermionic harmonic oscillator
Free scalar eld theories reduce to a product of harmonic oscillators. Fermionic free theories
reduce to a product of fermionic harmonic
Physics 610
1
Homework 5 Solutions
High-order Feynman diagrams
Consider the theory of one real scalar eld with Lagrangian density
m2 2
1
4 .
L[, ] =
2
2
24
1.1
(1)
6 external legs
In class we consid
Physics 610
Homework 1
Due Wed. 19 September 2012
1
4-vector notation and Maxwell equations
1.1
Problem
The purpose of this problem is to get you used to index notation and in particular to 4-vector
n
Physics 610
Homework 2
Due Thurs 27 September 2012
1
Commutation relations
In class we found that
(x) , (y) = i 3 (x y)
(1)
and then dened
(pm ) L3/2
d3 xeipm x (x)
(2)
and likewise for (pm ). Show th
Physics 610
1
Homework 3 Solutions
Projection operators
Consider the free eld theory of one scalar of mass m. Dene the state
|p = a |0 .
p
(1)
(Recall that ak , a = 2p (2 )3 3 (k p) and that ak |0 = 0
Question 1
Being trapped in situations where moral and ethical values are questioned can make ones
decisions and actions more challenging. Melchin proposed five questions that an
individual can ask th