Unformatted text preview: ≤ x ≤ L described by the action S = Z d t Z L d x ³ 1 2 ( ∂ μ φ )( ∂ μ φ )m 2 2 φ 2κ 3 φ 3λ 4 φ 4 ´ + Z d t M 2 [ φ ( t,L )] 2 , where m , κ , λ , and M are constants. By demanding that δ S = 0 for an arbitrary variation δφ ( t,x ) (with the only restriction being δφ ( t,x ) → 0 for t → ±∞ ), derive (a) the boundary condition for φ at each boundary x = 0 and L , (b) the equation of motion for φ in the “bulk” 0 < x < L , and (c) general solutions of the equation of motion satisfying the boundary conditions, assuming m = κ = λ = 0 for simplicity but still with M 6 = 0. 1...
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 Fall '10
 Okui
 Special Relativity, Boundary value problem, Spacetime

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