lec16 - Lecture 16 8.251 Spring 2007 Lecture 16 Topics Light-cone elds and particles Reading Sections 9.5-10.1 Space-lling D-brane x = x 0 1 2 0 i 2 ein

# lec16 - Lecture 16 8.251 Spring 2007 Lecture 16 Topics...

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Lecture 16 8.251 Spring 2007 Lecture 16 - Topics Light-cone fields and particles Reading: Sections 9.5-10.1 Space-filling D-brane µ α µ x µ ( τ, σ ) = x 0 + 2 α α µ 0 τ + i 2 α 1 n e inτ cos( ) n n =0 α µ = 2 α p µ 0 µ α µ = na n n α µ = na µ n n n x ( τ, σ ) = βα ( n p ) τ · · n · P τ constant along string. x ¨ µ x µ �� = 0 1 ∂x µ P µ σ = 2 πα ∂σ 1 ∂x µ τ = µ P 2 πα ∂τ ( ˙ x ± x ) 2 = 0 µ x ˙ µ ( τ, σ ) = 2 α α 0 µ + 2 α a n e inτ cos( ) n =0 α µ = 2 α n e inτ cos( ) n Z α µ n =0 x µ ( τ, σ ) = i 2 α n e inτ sin( ) α µ = i 2 α n e inτ sin( ) n Z µ α µ e in ( τ ± σ ) x ˙ ± x µ = 2 α n n Z Let ηµ = (1 / 2 , 1 / 2 , 0 , 0 , . . . ) 1
Lecture 16 8.251 Spring 2007 1 n · x = 2 ( x 0 + x 1 ) = x + n p = p + · x + ( τ, σ ) = βα p + τ Open Strings: x + = 2 α p + τ x + = 0 0 α + = α + for n = 1 , . . . , n n Coordinates of string: ( x + , x , x I ) I = 2