文档介绍：The wonders of supersymmetry:
from quantum mechanics, topology,
and noise, to (maybe) the LHC
Erich Poppitz
/
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High-Energy Physics Literature Database
find title SUPERSYM# or title SUSY# or title MSSM or
title NMSSM or title NNMSSM
Nov. 21, 2005 Paper 1 to 25 of 13979
Oct. 18, 2007 Paper 1 to 25 of 15656
what is supersymmetry?
what is it good for?
why we have studied it for so long?
(will we ever stop?)
supersymmetry is a quantum mechanical space-time
symmetry, which relates bosons and fermions
curiously, it was not discovered in quantum mechanics
first, but in string theory and quantum field theory
Ramond 1971
Golfand, Likhtman 1972
Wess, Zumino 1974
nevertheless, some of its most important applications
to date involve quantum mechanics
Witten 1981
moreover, supersymmetric quantum mechanics has all
features that make it clear why supersymmetry is
interesting to particle physicists, as well as to other fields
the harmonic oscillator
in quantum mechanics, we know that
implies
bosons: commutation relations
between creation and annihilation operators
energy spectrum of bosonic oscillator
what are fermions? they obey Pauli principle!
explicitly:
fermions: mutation relations
between creation and annihilation operators
the -1/2 may look cooked-up, but es from
quantizing the Dirac equation+C-symmetry
we’ll simply define fermionic oscillator that way
energy spectrum of fermionic oscillator
add them up: the supersymmetric oscillator
Proof:
introducing: the supersymmetry generators
this is not as silly as it looks!