It’s the Standard Model of particle physics. A summary may be found here: http://www-pnp.physics.ox.ac.uk/~barra/teaching/standard-model.pdf

A more comprehensive reference would be the book ``Quantum Field Theory and the Standard Model" by Matthew Schwartz.

Some on-line lecture notes can be found here: http://www-hep.colorado.edu/~degrand/Tasi/standard.html

See also: http://www.damtp.cam.ac.uk/user/ho/SM.pdf

In addition to the previous answer, if you want an introductory book not advanced one, I recommed: Griffiths' Introduction to elementary particles.

The interaction is not always precisely known.

The best known are electromagnetic interaction between charged particles,

with Coulomb form.

However the interaction between two protons would have a nuclear short ranged attractive part whose form is not known exactly, as well as repulsion at very close range. (apart from the Coulomb interaction)

I started following this thread for my own education with the hopes that any of us can ask our own questions here and get some answers. I am familiar with elementary quantum mechanics which is a non-relativistic treatment of a single particle interacting with a given potential energy function produced by a fixed (given) environment. I don't understand quantum field theory and searched for a book with a title like "Quantum Field Theory for Dummies". The closest thing that I could find to that is 300 pages long. I have a question that maybe has a quick answer that can be given without reading 300 pages. My understanding from the first few chapters of that book is that what was a wave function in elementary quantum mechanics becomes an operator in quantum field theory. The operator is a function of time and space coordinates so there is a different operator for each space-time point. What I don't understand, even after reading a few chapters, is what that operator operates on. In elementary quantum mechanics, operators operate on elements (state vectors) of a vector space (a Hilbert space) and I know the mathematical significance of these elements (state vectors) that the operators operate on. I have no idea of what the entities are that the quantum field theory operators operate on. Can this be explained to a person with my level of education in a few paragraphs?

L.D. Edmonds,

Quantum field theory requires a significant mathematics background as one has to consider spinor bundles (bundles modeled on a Clifford algebra) and other such geometric generalizations as the price of admission. One is required to work in the Lorentz metric as the tangents spaces are Minkowski spaces. That is required to make QFT compatible with relativity. Most text don't give the mathematical foundations necessary in sufficient rigor but what they do give is takes up the space of the physical motivations. However, this one at least tires to strike a good balance with sufficient motivation.

https://www.amazon.com/Quantum-Field-Theory-Gifted-Amateur/dp/019969933X/ref=sr_1_2?Adv-Srch-Books-Submit.x=0&Adv-Srch-Books-Submit.y=0&dchild=1&keywords=quantum+field+theory&qid=1635607886&qsid=144-8271784-0452340&s=books&sr=1-2&sres=1107034736%2C019969933X%2C0201503972%2C3948763011%2C0521670535%2C0691140340%2C0521864496%2C052167056X%2C1108972357%2C0691149089%2C0984513957%2C0486445682%2C9811239886%2C9814635502%2C3319374850%2CB08HYNK7TP%2C1108486215%2C019883831X%2C3030128776%2C0226870278&srpt=ABIS_BOOK&unfiltered=1

The good news is it is in the 20 to 30 USD range.

In some forms of field theory (axiomatic) you use creation and destruction operators acting on a Fock state of occupation numbers.

A quantum state for electrons with a given spin only holds up to one electron.

If the state holds none, a creation operator indexed for that state will create one.

A destruction operator on a full state will empty it.; on an empty state will return zero. Create on a full state will return zero.

Then see how the wave function becomes an operator, linear combination of such operators.

Complicated enough stuff, but about the simplest within that scenario.

On the other hand states for bosons like photons can store any number of photons in the same state.

You work up to this consulting things like Exclusion Principle, Fermi and Bose statistics, Feyman diagrams and the like.

I wouldent pay that much attention to the math till you have the Physics down.

The Dirac model for electrons is also a starting jump point for this (The so called relativistic QM).

Then read the classification that the standard model gives for elementary particles.; the main characteristics for nuclear particles like n or p.

weak decays and so on.

Learn well the basic special relativity.

That will prevent you from becomming one of those up in the air over mathematicised field theorists.(Generally defined as some mixture of QM and Relativity) which dont get along with each other that well.

Hi Juan Weisz . You mentioned creation and destruction operators and I wonder if you will answer another question. I have seen these operators in the context of second quantization which describes force fields in terms of particles (e.g., photons). I was never clear about the similarities or differences between second quantization and quantum field theory (QFT). My understanding, from very little education, is that QFT describes all particles (material and force-carriers) as disturbances in fields. I guess that there are creation and destruction operators in the context of QFT but these operators create or remove field disturbances. Is that correct? Is my understanding of second quantization versus QFT correct?

Dear Juan Weisz,

Would you present the destruction operator explicitly or indicate references where it can be found explicitly?

You could consult Quantum Mechanics by Leonard Schiff ( a book)

One of the later chapters deals with Quantization of Fields, as far as the electromagnetic field. This leads to Photons. It is fairly understandable in this reference.

The idea is that quatizing fields leads to particles.(However particle physics is far broader than this) It uses creation and destruction of photons.

Second quantization starts when think of many particles and use the wave fnction as operator, rather than just function. I guess it is a small subset of QFT or particle physics.

Thank you Juan Weisz . I have the book by Schiff but never looked at the chapter you mentioned (Chapter 14) and never understood the quantization of a wave function. A quick glance tells me that this chapter explains it all. Thanks for suggesting it.