In this chapter we wish to show that the Brownian bridge may be reconstructed from a denumerable set of independent Gaussian random variables other than the ones used in the bisection algorithm considered in Sect. 3.5. For it is possible to give meaning to the concept of Fourier decomposition of Brownian motion and to prove statistical independence of the relevant (random) Fourier coefficients. The motive for introducing this new structural element is that it allows us to approximate or even evaluate path integrals in a more systematic fashion.
KeywordsHarmonic Oscillator Transition Amplitude Fourier Coefficient Path Integral Imaginary Time
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