Explaining Equation (2.8) from Equation (2.6)

[Lapidus]

Could someone explain to me how equation (2.8) follows from equation (2.6) on page 20 (pdf page 21) http://www.physics.utoronto.ca/~luke/PHY2403/References_files/lecturenotesII.pdf"

It must be easy.

thanks!

 

[Bill_K]

He derives (2.8) from (2.6) by using (2.9)! Which in turn follows from (2.10). You just have to read it backwards...

 

[Lapidus]

Many thanks, Bill_K!

So do I get Z[J(y)]= 1 + Z[J(x_1)] +(1/2)Z[J(x_1)]Z[J(x_2)] + (1/3)Z[J(x_1)]Z[J(x_2)]Z[J(x_3)] + ... ? Does that make sense?

Tony Zee expands Z(J) in his book, too, http://press.princeton.edu/chapters/s9227.pdf" first line of equation (13). But why does he not have the integrals over x in his expansion? Has that something to do with the Z(0,0) in front?

again, thank you

 

[Lapidus]

It's a typo!

Zee forgot to put the integrals in the equation. I checked, in the second edition they are there.

But back to my initial problem in the lecture notes from Michael Luke. When I insert 2.6 into 2.8 do I get Z[J(y)]= 1 + Z[J(x_1)] +(1/2)Z[J(x_1)]Z[J(x_2)]+(1/3)Z[J(x_1)]Z[J(x_2)]Z[J(x_3)] + ... ?

I would welcome any further hints. thank you