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# Bz in fact it makes problem completely intractable

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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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## This document was uploaded on 03/03/2014.

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