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I'm reading a course in Introduction to QFT and I'm stuck at a problem.

I'm hoping someone here could point me in the right direction or say if my assumptions are incorrect.

Derive the Feynman rules and all diagrams at tree-level for [tex]\lambda \phi^3[/tex] theory using Wick's theorem.

My own questions:

To what n do you take the n-point correlation function [tex]\tau(x_1,x_2,...,x_n)[/tex]?

How does one draw a simple tree-level Feynman diagram depending if you know the interaction term [tex]L_i_n_t[/tex] or [tex]H'_I[/tex]

Is there something I haven't understood yet or is there something I'm forgetting about Feynmans rules and diagrams

The correlation function:

[tex]\tau(x_1,x_2,...,x_n) = \langle0\left\right| T{\phi_i_n(x_1)\phi_i_n(x_2)...\phi_i_n(x_n)exp(-i\int H'_I(t')dt')}\left|\right0\rangle[/tex]

to all orders in pertubation theory and where

[tex]H'_I = \int d^3 x \lambda \phi^3 / 3![/tex]

I've read (in Peskin & Schroeder) that higher than [tex]n = 2[/tex] correlation functions have to be solved using brute force (doesn't understand) and thought that it has to be [tex]n = 2[/tex] otherwise it's beyond the scope of the course.

For that case however, for the first order of pertubation in [tex]\lambda[/tex], there are an odd number of [tex]\phi[/tex]'s and therefore they can't give any contributions due to normal-ordering. Right?

There is, however, an even number of [tex]\phi[/tex]'s for the second order in the pertubation.

Do I have to take to the second order of [tex]\lambda[/tex] to get the diagrams?

As for the rules: I've understood that the zeroth order in pertubation just gives the propagator (for [tex]n = 2[/tex]) and that there has to be a 3-way vertex (insted of the 4-way vertex for [tex]\lambda \phi^4[/tex] theory). Should they also have the same "value" when constructing the [tex]M[/tex] matrix?

The diagrams draw for [tex]\lambda \phi^4[/tex] theory in Peskin & Schroeder's "An Introduction to Quantum Field Theory" har straight 2 point lines (with some loops), how does one go from these to a tree-level diagram?

I'd also appreciate any tips on books that deal with [tex] \phi^3 [/tex] theory.

I'm hoping someone here could point me in the right direction or say if my assumptions are incorrect.

## Homework Statement

Derive the Feynman rules and all diagrams at tree-level for [tex]\lambda \phi^3[/tex] theory using Wick's theorem.

My own questions:

To what n do you take the n-point correlation function [tex]\tau(x_1,x_2,...,x_n)[/tex]?

How does one draw a simple tree-level Feynman diagram depending if you know the interaction term [tex]L_i_n_t[/tex] or [tex]H'_I[/tex]

Is there something I haven't understood yet or is there something I'm forgetting about Feynmans rules and diagrams

## Homework Equations

The correlation function:

[tex]\tau(x_1,x_2,...,x_n) = \langle0\left\right| T{\phi_i_n(x_1)\phi_i_n(x_2)...\phi_i_n(x_n)exp(-i\int H'_I(t')dt')}\left|\right0\rangle[/tex]

to all orders in pertubation theory and where

[tex]H'_I = \int d^3 x \lambda \phi^3 / 3![/tex]

## The Attempt at a Solution

I've read (in Peskin & Schroeder) that higher than [tex]n = 2[/tex] correlation functions have to be solved using brute force (doesn't understand) and thought that it has to be [tex]n = 2[/tex] otherwise it's beyond the scope of the course.

For that case however, for the first order of pertubation in [tex]\lambda[/tex], there are an odd number of [tex]\phi[/tex]'s and therefore they can't give any contributions due to normal-ordering. Right?

There is, however, an even number of [tex]\phi[/tex]'s for the second order in the pertubation.

Do I have to take to the second order of [tex]\lambda[/tex] to get the diagrams?

As for the rules: I've understood that the zeroth order in pertubation just gives the propagator (for [tex]n = 2[/tex]) and that there has to be a 3-way vertex (insted of the 4-way vertex for [tex]\lambda \phi^4[/tex] theory). Should they also have the same "value" when constructing the [tex]M[/tex] matrix?

The diagrams draw for [tex]\lambda \phi^4[/tex] theory in Peskin & Schroeder's "An Introduction to Quantum Field Theory" har straight 2 point lines (with some loops), how does one go from these to a tree-level diagram?

I'd also appreciate any tips on books that deal with [tex] \phi^3 [/tex] theory.

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