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Unformatted text preview: So how does it stick them together? It s like electromagnetism, but with matrices for fields.
the
Ez
Bx
B = By Right?!
Going from numbers to matrices shouldn t make too much difference.
Bz
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 the first lecture. You should integrate over allProb ∼ paths that a particle)
possible
exp (iS/
Bz this translates to the fact that you should integrate
takes. In particle physics,
all ﬁelds over all possible configurations of the electric and magnetic fields. Prob ∼
exp (iS/) all ﬁelds S=
d4 x Tr E 2 − B 2 References vectors...but not when the
We can do this sum when the fields are normal vectors...
elements of the vectors are matrices!
S = [1] d4 x E 2 andB 2
Gibbons − Rychenkova, 9608085 QCD is Hard!
Clay Mathematics problem: $1 million
Serious Supercomputers
Even the simplest question is immensely
difficult: what does empty space look
like? Prob ∼ Confinement
exp (iS/)
all ﬁelds 4 2 2 S = d x Tr E − B
The quarks can never escape the proton or neutron.
If you try to pull a quark away, a long string forms pulling it back in. The
force between two quarks is linear: F ∼ r . This is called confinement References
[1] Gibbons and Rychenkova, 9608085
[2] Kapustin and Strassler, 9902033
This is why quarks stick together in so many ways.
To prove confinement from the equations of QCD is one of the most
important open problems in theoretical physics.
An Aside:4 xStrings B 2 QCD
S = d Tr E 2 − in
Homework exercise: consider two relativistic particles with separation r,
and an attractive force F=r.
Show that whenF ∼ r
the angular momentum, J, is large, the energy of a the
spinning particles, attached by a string, scales as E∼ √ J But since E=mc2, this gives a
relationship between mass and angular
momentum of particles.
This
the beginning of string
c...
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 Spring '14

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