- #1
Chris.X
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Hi
I am struggling to justify
D(x-y) \approx e^{-i m t} as t \rightarrow \infty
from
\int dE \sqrt{E^2-m^2} e^{-i E t}.
I thought I might get some insight from discretizing, as
e^{-i m t} \sum_{n=0}^{\infty} \epsilon \sqrt{ n \epsilon ( 2 m + n \epsilon ) } e^{-i n \epsilon t}
but I don't understand how to approximate or take the limit of the sum.
I also tried to work backwards from
G : (E^2-m^2)^{3/2} e^{-i E t}
and replacing extra E's with d/dt's and ended up with a differential equation
for the result,
G = i [ t (d^2/dt^2 + m^2) + 3 d/dt ] D(x-y)
but I am having trouble putting the pieces together to solve it.
Assistance would be greatly appreciated.
I am struggling to justify
D(x-y) \approx e^{-i m t} as t \rightarrow \infty
from
\int dE \sqrt{E^2-m^2} e^{-i E t}.
I thought I might get some insight from discretizing, as
e^{-i m t} \sum_{n=0}^{\infty} \epsilon \sqrt{ n \epsilon ( 2 m + n \epsilon ) } e^{-i n \epsilon t}
but I don't understand how to approximate or take the limit of the sum.
I also tried to work backwards from
G : (E^2-m^2)^{3/2} e^{-i E t}
and replacing extra E's with d/dt's and ended up with a differential equation
for the result,
G = i [ t (d^2/dt^2 + m^2) + 3 d/dt ] D(x-y)
but I am having trouble putting the pieces together to solve it.
Assistance would be greatly appreciated.
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