1
Content of the course
Quantum Field Theory by M. Srednicki, Part 1.
2
Combining QM and relativity
We are going to keep all axioms of QM:
1. states are vectors (or rather rays) in Hilbert space.
2. observables are Hermitian operators and their values are
1
Free real scalar eld
The Hamiltonian is
1
3
H = d xH =
d 3 x p( x) 2 + ( ) 2 + m2 2
2
Let us expand both and p in Fourier series:
d3 p
d3 p
i p x
(t, x) =
(t, x)e , p(t, x) =
p(t, x)eipx .
2 (p)
2 ( p)
where (p) = p2 + m2 . Then:
1
d3 p
2
(p)|2 (p)2 .
Week 1 (due Oct. 9)
Reading: Srednicki 1.1 (i.e. section 1 of Part 1) and Notes 1.
1. Consider the bosonic Fock space corresponding to the 1-particle Hilbert
space H1 = L2 (R3 ). Let (x) and (x) be the standard annihilation and
creation operator for boson
Week 2 (due Oct. 16)
1. Let be a free real scalar eld. The commutator (x) = [(x), (0)]
is a c-number (i.e. it is proportional to the identity operator in Fock space)
and is known as the commutator function for . Compute the commutator
function for the cas
Week 3 (due Oct. 23)
1. (a) Consider free complex scalar eld with mass m. The expansion
of the eld in terms of creation and annihilation operators is given in eq.
(3.38) in Srednicky (Problem 3.5). Invert this formula and express ak , bk , a
k
and b in te
Week 4 (due Oct. 30)
1. The transition amplitude in nonrelativistic Quantum Mechanics is
dened by
K (q , q ; T ) = q |eiHT |q .
Here H is the usual Hamiltonian, i.e.
H=
p2
+ V (q ).
2m
(a) Compute K (q , q ; T ) for the free particle (V = 0) by inserting