What are the next steps in constructing \phi_{3}^{4} in Field Theory?

[DarMM]

I previously took part in two separate threads where I slowly went through various field theories from a rigorous perspective. I would like to restart the discussion. Here are the two previous threads for anybody who would like to take part this time:

Thread 1
The pages from 12 on (and especially 15 and 16) are the most relevant.

Also:
Thread 2

So far \phi_{2}^{4} has been constructed. For \phi_{3}^{4} I have built the appropriate Hilbert Space on which the Hamiltonian is a well defined operator (it doesn't produce infinities in loose language) with no ultraviolet cut-off. However I must next show that it is self-adjoint and semi-bounded. After that I will need to remove the volume cut-off.

 

[A. Neumaier]

For \phi_{3}^{4} I have built the appropriate Hilbert Space on which the Hamiltonian is a well defined operator (it doesn't produce infinities in loose language) with no ultraviolet cut-off. However I must next show that it is self-adjoint and semi-bounded. After that I will need to remove the volume cut-off.

Welcome back! I am looking forward to learn about the next step of the ladder!