PPT Slide

Wave Maps

NONLINEAR RELATIVISTIC FIELD THEORIES

?: IR n+1 M

?I + ?IJK (?) Q0(?J,?K ) = 0


Q0(?,?) = - ? t ? ? t ? + ? i ? i ? ? i ?

Critical exponent sc = n/2

Subcritical n = 1

Critical n = 2
Supercritical n ? 3

E = (|? t ?(t,x)|M2 + ? i| ? i ? (t,x)|M2 )dx

Scaling
x0= t, x1, …, xn L

? L0
E Ln-2
n - 2 = 0

?

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