- Summary
- On the second quantisation of potential term associated with inter-particle interactions

In Bundell's QFT book, the second-quantised, pairwise interaction potential was defined as:

in a later step, this was re-written in a momentum-space representation

1. I don't understand why it goes from ##V(x, y)## to ##V(x-y)##, why do we consider only this form of interaction potentials?

2. Also, could someone show how the expression for ##\hat{V}## derive from the general form of the second-quantised two particle operator below?

Thanks in advance!

in a later step, this was re-written in a momentum-space representation

1. I don't understand why it goes from ##V(x, y)## to ##V(x-y)##, why do we consider only this form of interaction potentials?

2. Also, could someone show how the expression for ##\hat{V}## derive from the general form of the second-quantised two particle operator below?

Thanks in advance!