The Path Integral, Perturbation Theory and Complex Actions

• Now for a displaced point mass at a relative
fixed position we have
oves only along ∫ the line that sepanstant
= −4m unit vector, and shifting the
⃗r
dt ′ (β µ (t ′ )β ν (t ′ ) − (1/2)η µν ) δ(t − t′ −|⃗x − ⃗r(t ′ ) − ⃗r|)
|⃗x − ⃗r(t ′ ) − ⃗r|
ce
M
•
moves
ˆr
in the only former along we have the line that (5) sepaa
constant t) 2 unit vector, and shifting the
elds
have r(t t t) = ⇥t ′ r(t) + |⃗x −ṙ(t)r(t)/v ⃗r(t ′ )| g
GM ˆr
• GM
⇥ while ˆr at the second point we have
r 2 (t) (1 + 2ṙ(t)/v (5)
r(t t) 2 g). (6)
cillators ll, we have with r(t t ⃗r r(t) = t =r(1 t) ′ + ⇥|⃗x r(t) + −⇤ ⃗r(t sin(⌃t ṙ(t)r(t)/v ′ ) − ⃗r| g
t the origin, and that the motion is
GM ˆr
Tuesday, 2 April, 13