General · Language

QFT – How many fields are there?

[Draft] [“Building a ‘verse” series]

Ever since I started reading about Quantum Field Theory (QFT), I was interested in how physicists talk about fields. And the multiplicity of fields. And how quantum fields compare to classical fields.

So, as I’ve written elsewhere, the basic notion is that every matter particle is an excitation (or localized vibration) in a field. Some visualizations help. Sometimes physicists just say there are lots of fields, sometimes dozens, sometimes one for every particle in the Standard Model. So, what’s the count?

According to quantum field theory, there are certain basic fields that make up the world, and the wave function of the universe is a superposition of all the possible values those fields can take on. — Carroll, Sean. The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (pp. 173-174). Penguin Publishing Group. Kindle Edition.

Reality is fields [post]: Sure enough, Carroll explains that space is full of fields, “at every point in space, there’s dozens of little vibrating fields … when you look at the fields closely enough they resolve into individual particles.” (Can we say particles are contextual realities?)

LiveScience: “Physicists Search for Monstrous Higgs Particle. It Could Seal the Fate of the Universe” by Paul Sutter, Astrophysicist, June 5, 2019

In our best conception of the subatomic world using the Standard Model, what we think of as particles aren’t actually very important. Instead, there are fields. These fields permeate and soak up all of space and time. There is one field for each kind of particle. So, there’s a field for electrons, a field for photons, and so on and so on. What you think of as particles are really local little vibrations in their particular fields. And when particles interact (by, say, bouncing off of each other), it’s really the vibrations in the fields that are doing a very complicated dance.

Fermilab‘s Don Lincoln talks about fields in this YouTube video:

Published on Jan 14, 2016
In modern physics theory, one can picture all subatomic particles as beginning with a field. Then the particles we see are just localized vibrations in the field. So, according to quantum field theory, the right way to think of the subatomic world is that everywhere- and I mean everywhere- there are a myriad of fields. Up quark fields, down quark fields, electron fields, etc. And the particles are just localized vibrations of the fields that are moving around. Theoretical physics simply imagines that ordinary space is full of fields for all known subatomic particles and that localized vibrations can be found everywhere. These fields can interact with one another, like two adjacent tuning forks. These interactions explain how particles are created and destroyed – basically the energy of some vibrations move from one field and set up vibrations in another kind of field.
Chart
Standard model of elementary particles: the 12 fundamental fermions and 5 fundamental bosons.

Notes

[1]

According to quantum field theory, there are certain basic fields that make up the world, and the wave function of the universe is a superposition of all the possible values those fields can take on. If we observe quantum fields—very carefully, with sufficiently precise instruments—what we see are individual particles. For electromagnetism, we call those particles “photons”; for the gravitational field, they’re “gravitons.” We’ve never observed an individual graviton, because gravity interacts so very weakly with other fields, but the basic structure of quantum field theory assures us that they exist. If a field takes on a constant value through space and time, we don’t see anything at all; but when the field starts vibrating, we can observe those vibrations in the form of particles. — Carroll, Sean. The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (p. 174). Penguin Publishing Group. Kindle Edition.

There are two kinds of quantum fields: fermions and bosons. Fermions are the particles of matter; they take up space, which helps explain the solidity of the ground beneath your feet or the chair you are sitting on. Bosons are the force-carrying particles; they can pile on top of one another, giving rise to macroscopic force fields like those of gravity and electromagnetism. Here is the complete list, as far as the Core Theory is concerned:

Fermions

1. Electron, muon, tau (electric charge –1).

2. Electron neutrino, muon neutrino, tau neutrino (neutral).

3. Up quark, charm quark, top quark (charge +2/3).

4. Down quark, strange quark, bottom quark (charge –1/3).

Bosons

1. Graviton (gravity; spacetime curvature).

2. Photon (electromagnetism).

3. Eight gluons (strong nuclear force).

4. W and Z bosons (weak nuclear force).

5. Higgs boson.

— Carroll, Sean. Ibid (pp. 433-434), Appendix: The Equation Underlying You and Me

[2] Wiki

QFT treats particles as excited states (also called quanta) of their underlying fields, which are—in a sense—more fundamental than the basic particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding fields. Each interaction can be visually represented by Feynman diagrams, which are formal computational tools, in the process of relativistic perturbation theory.