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Unformatted text preview: X ﬂuc ( t = t ) = 0. Show f ( t ) = X l e i S ( l ) winding ( t ) ¯ h × Z [ D X ﬂuc ] e i S ¯ h = c ( t ) X l e i S ( l ) winding ( t ) ¯ h . (2) Calculate S ( l ) winding ( t ) and c ( t ). In obtaining the latter observe that this is just the same result needed to correct the classical result for the free particle on the real line R . (c)Show that the results in part (a) and (b) are equivalent by using the Poisson resummation formula ∞ X n =-∞ e-απ 2 n 2 = 1 √ πα ∞ X l =-∞ e-l 2 α . (3) (d) Prove f ( t ) is periodic in time. This is diﬀerent than the real line case....
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- Spring '09
- free particle, periodic boundary conditions, Path Integral Method