You can absorb these divergences from self contractions (‘search for cephalopod Feynman diagrams and ‘complete normal ordering’ in google) into your bare couplings (the necessary bare couplings need to exist in your theory if it is renormalisable). In the g=0 example the same applies, but now the bare coupling is a “cosmological constant” that you can include or ignore depending on the question and background spacetime of interest.

So yes, these are related to renormalisation of qft, but sometimes these diagrams do not affect the beta functions and so do not affect the RG flow in which case they can be dropped. They are usually identified with normal ordering (more generally ` complete normal ordering’) issues, which is a type of renormalisation but often more mild. These diagrams can affect and shift the vacuum around which you are doing perturbation theory if it so happens that you chose the wrong vacuum in your perturbation expansion.

In general, the procedure that removes all these self contraction diagrams (which automatically also ensures you are doing perturbation theory around the exact vacuum) is `complete normal ordering’.

Ellis, J., Mavromatos, N. & Skliros, D., Complete Normal Ordering 1: Foundations, Nucl.Phys. B909 (2016) 840-879

You can absorb these divergences from self contractions (‘search for cephalopod Feynman diagrams and ‘complete normal ordering’ in google) into your bare couplings and wavefunction renormalisation (the required bare couplings need to exist in your theory if it is renormalisable). In the g=0 example the same applies, but now the bare coupling is a “cosmological constant” that you can include or ignore depending on the question and background spacetime of interest.

So yes, these are related to renormalisation of qft, but sometimes these diagrams do not affect the beta functions (i.e. do not affect the RG flow) in which case they might be dropped. They are usually identified with normal ordering (more generally ` complete normal ordering’) issues, which is a type of renormalisation but often more mild. These diagrams can affect and shift the vacuum around which you are doing perturbation theory if it so happens that you chose the wrong vacuum in your perturbation expansion.

In general, the procedure that removes all these self contraction diagrams (which automatically also ensures you are doing perturbation theory around the exact vacuum) is `complete normal ordering’.

Ellis, J., Mavromatos, N. & Skliros, D., Complete Normal Ordering 1: Foundations, Nucl.Phys. B909 (2016) 840-879

You can absorb these divergences from self contractions (‘search for cephalopod Feynman diagrams and ‘complete normal ordering’ in google) into your bare couplings (the necessary bare couplings need to exist in your theory if it is renormalisable). In the g=0 example the same applies, but now the bare coupling is a “cosmological constant” that you can include or ignore depending on the question and background spacetime of interest.

So yes, these are related to renormalisation of qft, but sometimes these diagrams do not affect the beta functions and so do not affect the RG flow in which case they can be dropped. They are usually identified with normal ordering (more generally ` complete normal ordering’) issues, which is a type of renormalisation but often more mild. These diagrams can affect and shift the vacuum around which you are doing perturbation theory if it so happens that you chose the wrong vacuum in your perturbation expansion.

In general, the procedure that removes all these self contraction diagrams (which automatically also ensures you are doing perturbation theory around the exact vacuum) is `complete normal ordering’.

You can absorb these divergences from self contractions (‘search for cephalopod Feynman diagrams and ‘complete normal ordering’ in google) into your bare couplings (the necessary bare couplings need to exist in your theory if it is renormalisable). In the g=0 example the same applies, but now the bare coupling is a “cosmological constant” that you can include or ignore depending on the question and background spacetime of interest.

So yes, these are related to renormalisation of qft, but sometimes these diagrams do not affect the beta functions and so do not affect the RG flow in which case they can be dropped. They are usually identified with normal ordering (more generally ` complete normal ordering’) issues, which is a type of renormalisation but often more mild. These diagrams can affect and shift the vacuum around which you are doing perturbation theory if it so happens that you chose the wrong vacuum in your perturbation expansion.

In general, the procedure that removes all these self contraction diagrams (which automatically also ensures you are doing perturbation theory around the exact vacuum) is `complete normal ordering’.

Ellis, J., Mavromatos, N. & Skliros, D., Complete Normal Ordering 1: Foundations, Nucl.Phys. B909 (2016) 840-879