- #1
friend
- 1,452
- 9
I'm reading Quantum Field Theory Of Point Particles And Strings, by Brian Hatfield, chapter 9 called Functional Calculus. But he seems to assume some famiality with the subject. I'm intriqued by his notation. He uses notation for functional derivatives almost as if it were ordinary derivatives; he uses the notation:
[tex]\[
\frac{{\delta F[a]}}{{\delta a(x)}}
\][/tex], [tex] \[
\frac{{\delta ^2 G[a]}}{{\delta a(y)^2 }}
\][/tex], and [tex] \[
\int {\Delta a\,\,e^{ - F[a]} }
\]
[/tex].
I'm looking for a more complete development of these ideas using this kind of notation. I wonder if it is developed enough to solve for Functionals F[a], like differential equations solve for functions. It makes me wonder if, say, the functional Lagrangian of physics can be derived on first principles using these methods. Any guidance would be appreciated. Thanks.
[tex]\[
\frac{{\delta F[a]}}{{\delta a(x)}}
\][/tex], [tex] \[
\frac{{\delta ^2 G[a]}}{{\delta a(y)^2 }}
\][/tex], and [tex] \[
\int {\Delta a\,\,e^{ - F[a]} }
\]
[/tex].
I'm looking for a more complete development of these ideas using this kind of notation. I wonder if it is developed enough to solve for Functionals F[a], like differential equations solve for functions. It makes me wonder if, say, the functional Lagrangian of physics can be derived on first principles using these methods. Any guidance would be appreciated. Thanks.