Lecture 8 Notes: Ultraviolet Divergence
2.3: REMOVING ULTRAVIOLET DIVERGENCES
3
Let us consider the same example, but now in d = 6, where the coupling constant g becomes dimensionless.
g
2
(p ) =
2
2
1
dx
d
d
2
2
+ D)
(2) (q
0
2
1
d qE
(1)
,
E
2
with D =
Lecture 5 Notes: Auxillary Field
DADCaDCae
a
Z=
with
]
[
2
1
iS
ef f
a
[A
,C,C]
,
(1)
fa(A(x) _ ]
b(y) _=0 Cb(y),
(2)
+ d xd y Ca(x)
_
a
a
_
4
is the pure Yang-Mills action. S0 [A] is invariant
F F
4
4
2
Seff A, C, C
= S0 [A]
d x fa (A)
1
where fa(A) is
Lecture 3 Notes: Finite Parallel Transport
We begin with some comments concerning gauge-symmetric theories:
1.
A U(1) local symmetry leads to the field A(x), mediating interactions between the charge fields i(x).
2.
No mass term is allowed for A or the ga
Lecture 4 Notes: Degrees of Freedom
Gauge symmetry is not a true symmetry, but a reflection of the fact that a theory possesses redundant degrees of freedom. A gauge symmetry implies the existence
of dierent field configurations which are equivalent. For
Lecture 6 Notes: Mass Renormalizations
Now that we have studied almost all known quantum field theories, we return to studying physical observables in
these theories. We will start with the simplest object:
0|O(x)O(y) |0 ,
(1)
that is, the vacuum two-poin
Lecture 2 Notes: Internal Symmetry Groups
Figure 1: An element of the manifold of the Lie group G, and the Lie algebra g as the tangent space of the identity element.
Some facts about Lie groups and Lie algebras:
3
3
1.
Dierent Lie groups can have the sam
Lecture 1 Notes: Intro to Course
In 8.323, we have studied the quantum theory of:
1.
Scalar fields, spin-0,
2.
Dirac fields, spin- 2 ,
Maxwell fields, spin-1.
1
3.
The last two fields are the content of quantum electrodynamics, an extremely successful des
Lecture 9 Notes: Electrodynamics
3.1: RENORMALIZED LAGRANGIAN
Consider the Lagrangian of quantum electrodynamics in terms of the bare quantities:
1
B
L =
4
F F
B
iB(
B
(ieBA ) mB )B.
(1)
We use the convention:
cfw_ , = 2 ,
2
0 =1,
(2)
i = i,
0 =0,
,
Lecture 10 Notes: Lagrangian Theory
We now consider the Lagrangian for quantum electrodynamics in terms of renormalized quantities.
1
B
L = 4
1
F F
iB(
B
B
( ieBA)mB)B
iZ2(
= 4 Z3F F
m
m)Z2eA
.
We know from previous lectures that there is no mass term
iZ
GF(p) =
2
+
2
p
2
i
+m
2
i
2
d ( )
2
4m
,
2
p
(1)
i
+
Lecture 7 Notes: Dimensionless Equation
where the first term is the contribution from single-particle states, and the second term is the contribution from multi-particle states. From this, we have
Unit 1
1. What are the two parts of geology?
Its made up of
Physical is what makes up the earth now
Historical its the past of the earth
2. What are the steps of the scientific method?
The manner in which science operates insures honestly and insures th