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## Homework Statement

Consider the following real scalar field in two dimensions:

[itex] S = \int d^2 x ( \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2 - g \phi^3)[/itex]

What are the Feynman rules for calculating [itex] < \Omega | T(\phi_1 ... \phi_n ) | \Omega > [/itex]

2. Homework Equations

2. Homework Equations

For a phi-4 theory in 4d:

Each propagator contributes a Feynman propagator [itex] D_F (x-y) [/itex]

Each vertex z (4 lines to a point) contributes [itex] \frac{-i g}{4!} \int d^4 z [/itex]

**3. The Attempt at a Solution**

I just wanted to check my understanding is okay. Adapting the rules for a phi-4 theory (this is phi-3 theory, yes?):

Each propagator contributes a Feynman propagator [itex] D_F (x-y) [/itex] (same as before)

Each vertex (now only 3 lines to a point because it is a phi-3 theory) contributes [itex] \frac{-i g}{3!} \int d^3 z [/itex] (because phi-3 not phi-4) or [itex] \frac{-i g}{2!} \int d^2 z [/itex] (because 2d not 4d)

In Fourier space, one would integrate over momentum as [itex] \int \frac{d^3 p}{(2 \pi)^3} [/itex]

*Is this correct for adapting a phi-4 theory to phi-3?*

Does going from 4d to 2d change anything here I'm missing?

Does going from 4d to 2d change anything here I'm missing?

Thanks