This preview shows page 1. Sign up to view the full content.
Unformatted text preview: = Ey The D µ − m) ψ = 0
terms
(iγµelectromagnetic force is described inEz of electric and magnetic fields. Each of these is a 3vector Ex
E = Ey Ez Bx
B = By Bz Electric charges and magnets set up electric and
B
magnetic fields x erences
B = By
ibbonsLight waves arise as ripples of these fields
and Rychenkova, 9608085
Bz These light waves are actually made
apustin and Strassler, 9902033 of particles: these are photons kova, 9608085 (3) Forces, Matrices and Groups
ν Ex
E = Ey Ez
The D µ − m) ψ = work in the same way. There are
(iγµtwo nuclear forces0 (3) again analogs of electric and magnetic fields. Ex
E = Ey Ez erences Bx
B = By Bz Bx
Except now, each component of the vectors is itself a Hermitian matrix
B = By 2x2
for
ibbons and matrixBz the weak force
Rychenkova, 9608085
3x3 matrix for the strong force apustin and Strassler,associated to matrix groups: U(1), SU(2) and SU(3)
9902033
The three forces are
kova, 9608085 QCD
E = Ey Ez Ex
E = Ey The strong force (QCD) acts only on the quarks. So how does it stick Bx them
together? It s like electromagnetism, but with matrices for the fields.
Ez
B= B y Bz
Going from numbers to matrices shouldn t make too much difference. Right?!
In fact it makes problem completely intractable!!
the Bx
It s because the world is quantum, not classical. Recall the path integral from
B = By exp (iS/
the first lecture. You should integrate over all Prob ∼paths that a particle )
possible
Bz
takes. In particle physics, this translates to the fact that you ﬁelds integrate
all should
over all possible configurations of the electric and magnetic fields. Prob ∼
exp (iS/) all ﬁelds S=
d4 x E 2 − B 2 We can do this sum when the fields are normal vectors... References
S=
d4 x E 2 − B 2 [1] Gibbons and Rychenkova, 9608085 QCD
Ex
E = Ey Ez Ex
E = Ey The strong force (QCD) acts only on the quarks....
View
Full
Document
This document was uploaded on 03/03/2014.
 Spring '14

Click to edit the document details