[“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? 2, 17, 24, 25, or more?

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:

So, here’s a possible tally for the number of quantum fields:

- 2 (quantum electrodynamics [QED])
- 17 (Standard Model [above])
- 24 (Standard Model including all gluon colors) — 12 fermion fields and 12 boson fields
- 25 (24 + Graviton)
- Even more if include anti-particles?
- Even more if include handedness?

##### 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.

Fermionsare 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.Bosonsare 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 isthe 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

QFTtreats 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.

Even more fields than just one for each particle?

Science communicator and Forbes contributor Ethan Siegel discusses the QFT tally in this Forbes article, “Ask Ethan: Are Quantum Fields Real?” (Nov 17, 2018), which contains some useful visuals.

Forbes > Ask Ethan: Why Are There Only Three Generations Of Particles? by Ethan Siegel, Senior Contributor, Starts With A Bang Contributor Group (Sep 21, 2019).