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[tex]\sum^{\infty}_{n=0} \frac{(-i)^n}{n!} \int^{t}_{t'} dt_{1} dt_{2}...dt_{n} T(H_I(t_1)...H_I(t_n)) \equiv Texp[-i\int^{t}_{t'} dsH_I(s)][/tex]

My concern is that the integral

[tex]\int^{t}_{t'} dt_{1} dt_{2}...dt_{n} T(H_I(t_1)...H_I(t_n))[/tex]

is not raised to the power of 'n' so we can't really manipulate the expression on the LHS to fit:

[tex]exp(x)=\sum^{n=0}_{\infty}\frac{x^n}{n!}[/tex].

Also, why can you write a product of Hamiltonians as a single one - physically that makes no sense (to me anyway, a big qualification there!) ie why is H_{I}(t_{1})H_{I}(t_{2})...H_{I}(t_{n})=H_{I}(s)?

Thanks in advance...

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# Integral involving exponentials and the Time ordering operator

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