Different formulations of QFT

[ShayanJ]

As far as I understand now, there are at least three different formulations of QFT:

1) Second Quantization
2) Functional Formulation(where there is wave-functional which is a function of the field configuration and satisfies a functional Schrodinger equation)
3) Path Integral

Is there any other formulation out there?

Also, I know that QFT textbooks usually treat QED using second quantization and then turn to path integrals for non-abelian gauge theories(except for Bailin and Love that uses path integrals throughout). But the only textbook I know that spends some time on the functional formulation is Hatfield. Is there any other textbook that develops the functional formulation and uses it to calculate any physical quantity?

Thanks

 

[AndyW]

for your post! As a scientist familiar with quantum field theory (QFT), I can confirm that there are indeed multiple formulations of QFT. In addition to the three you mentioned, there are also others such as the operator formalism and the canonical quantization approach.

Regarding your question about other textbooks that focus on the functional formulation, I would recommend checking out "Quantum Field Theory for Mathematicians" by Robin Ticciati and "Quantum Field Theory: A Modern Perspective" by V. P. Nair. Both of these texts devote a significant portion to the functional formulation and its applications in QFT. Additionally, "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics" by Robert M. Wald also covers the functional approach in depth.

It is worth noting that while the functional formulation may not be as commonly used in textbooks, it is still an important approach in QFT and has been used to make significant contributions to the field. I hope this helps answer your question and provides you with some additional resources to explore.