# What are quarks and leptons in Quantum Field Theory?

Are the different quarks and leptons different kinds of oscillations of the same underlying quark field and lepton field, or same kinds of oscillations of different up, down and so on quark fields, and electron, electron neutrino and so on lepton fields? Or is there just a single field underlying all other fields?

• I think using SM (Standard Model) instead QFT would be a better formulation of your question. – peterh Apr 23 '17 at 20:51
• It is my understanding that QFT is the theoretical formulation of the Standard Model. Is this wrong? – Georgi Pavlov Apr 23 '17 at 23:07
• @GergoPavlov Check ViktorToth's answer. QFT describes any quantum field, SM is about the fields what we have in our Universe. – peterh Apr 23 '17 at 23:22
• @peterh Yes I did of course. I'm not sure I understand that part actually. Do you mean that QFT describes also abstract fields. How does it describe fields which don't exist in reality in the universe? QFT - a framework, describing fermionic and bosonic fields and their interactions; SM - describing specific lepton and quark (fermionic) fields and bosonic fields. Can you elaborate a little what exactly is the difference? – Georgi Pavlov Apr 23 '17 at 23:42

Quantum field theory in general doesn't know about quarks and leptons. It knows about bosonic and fermionic fields (e.g., scalar fields, vector fields, spinor fields) and their interactions.

So think of quantum field theory as a framework. The Standard Model of particle physics fills this framework with specific content: specific scalar, spinor and vector fields that are believed to represent physical reality.

The specific fields in the Standard Model are:

• doublets of left-handed charged and uncharged leptons;
• right-handed charged lepton singlets;
• doublets of left-handed up- and down-type quarks;
• right-handed up-type and down-type quark singlets;
• the $SU(2)\times U(1)$ gauge fields (four vector bosons) of the electroweak interaction;
• the $SU(3)$ gauge fields (eight massless gluons) of the strong interaction; and
• the Higgs field, responsible for electroweak symmetry breaking, the masses of three of the electroweak vector bosons, and fermion masses.

Lastly, the fermions (leptons and quarks) in the theory each have three generations.

So... a whole bunch of fields arranged in highly non-trivial ways, and the fundamental field content describes the theory before symmetry breaking. But the basic idea is that essentially yes, each different type of fundamental particle is a unit excitation of its own field, i.e., the up-quark field differs from the down-quark field, which differs from the top-quark field, the electron field differs from the muon field, and so on.

• WOW thank you. I've asked this question so many times and got all kinds of answers with so much different information, but never a straight answer to the question.. So a single field for each particle and not a single underlying field. Does string theory seek to derive all particles out of a single field? – Georgi Pavlov Apr 23 '17 at 23:00
• I am learning about QFT and found this helpful, but do you have any basic textbook references for it? – Bruce Long Mar 6 '18 at 13:38
• My "go to" book on QFT these days would be Peskin and Schroeder. – Viktor Toth Mar 6 '18 at 15:42