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suppose i want to calculate the propagator/transition amplitude which i can write as follows:

[tex](a,T|-a,-T)=\int_{-\infty}^\infty dx_1\int_{-\infty}^\infty dx_2(a,T|x_1,T_1)(x_1,T_1|x_2,T_2)(x_2,T_2|-a,-T)[/tex].

the situation is this:

i already have an approximation of [tex](a,T_{i-1}|-a,T_i)[/tex] which is qualitively different from [tex](a,T|-a,-T)[/tex], so that i can't simply calculate the latter by changing the time variable in the first expression. but i think it should be possible to use this information somehow to obatin the complete propagator. the problem is that i don't know how to deal with the intermediate integrations.

any help would be greatly appreciated.

(i'm using the path integral formalism for the calculation)

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# Propagator/transition amplitude through intermediate integrations

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