QFT: Srednicki's Book: What Does a(x) Represent?

[Hymne]

Hello! I have a question conserning Srednicki´s book on QFT. On page 27 he introduces a quantum field a(x) and its h.c. .
What does this field represent? What should I think of when he uses this field?

He writes the hamiltionian on the regular form but multiplicates with a(x) and its h.c. and then integrates over all of space...

It seems to be creation and annihilation operators for particles, but i don't really see the reason for this method.

 

[Daverz]

He does give you a way to interpret the operators:

"Thus we can interpret the state |0⟩ as a state of “no particles”, the state
a† (x1 ) |0⟩ as a state with one particle at position x1 , the state a† (x1 )a† (x2 )|0⟩
as a state with one particle at position x1 and another at position x2 , and
so on."

But it does seem to me that Srednicki is rather weak here on motivation. I would suggest watching the first few of Sidney Coleman's QFT lectures. There are also some good notes here:

http://www.physics.utoronto.ca/~luke/PHY2403/References.html

 

[The_Duck]

I think the point of this little demo is to make you work through a bit of operator algebra to see how a and a-dagger work algebraically, and how you can write a Hamiltonian in terms of creation and annihilation operators. In chapter 3 on quantization of scalar fields you get a derivation where these operators emerge naturally as important things.