Born-Infeld Theory:
Born-Infeld Theory:
Born-Infeld Theory:
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Scalar <strong>Born</strong>-<strong>Infeld</strong> theory in<br />
0+1 dim: integrability, “hidden” conformal symmetry<br />
and String <strong>Theory</strong><br />
1) Scalar BI theory in 1+1 dim = <strong>Theory</strong> of Bosonic String<br />
2 2<br />
L = 1− 1 −( ϕt − ϕx<br />
)<br />
⎛ t(,<br />
τσ)<br />
⎞<br />
μ ⎜ ⎟<br />
X =<br />
⎜<br />
x(,<br />
τσ)<br />
⎟<br />
⎜y= ϕ( t( τ, σ), x(<br />
τ, σ))<br />
⎟<br />
⎝ ⎠<br />
L =− ( XX � ′ ) −X�<br />
X ′<br />
2 2 2<br />
2) Weyl invariance (conformal symmetry) in the String language<br />
leads to the integral of motion in the BI theory
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