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QFT – How many fields are there?

John Healy

[“Building a ‘verse” series]

Chart
Standard model of elementary particles: the 12 fundamental fermions and 5 fundamental bosons.

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:

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.

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

  • 2 (quantum electrodynamics [QED]) – the electron field and the electromagnetic aka photon field
  • 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. 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.

7 thoughts on “QFT – How many fields are there?”

  1. Even more fields than just one for each particle?

    The correct formulation is more subtle. We have quantum fields that create left-handed particles, and separate quantum fields that create right-handed particles. The equations for those underlying fields are different. But once a particle (of either kind) is created, its interactions with the Grid can change its handedness. In the electroweak standard model, interactions of particles with the Higgs condensate do just that. — The Lightness of Being: Mass, Ether, and the Unification of Forces by Frank Wilczek

  2. 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.

    So how many fundamental quantum fields are there? Well, that depends on how you look at the theory. In the simplest QFT that describes our reality, the quantum electrodynamics of Julian Schwinger, Shinichiro Tomonaga and Richard Feynman, there are only two quantum fields: the electromagnetic field and the electron field. They interact; they transfer energy and momentum and angular momentum; excitations are created and destroyed. Every excitation that’s possible has a reverse excitation that’s also possible, which is why this theory implies the existence of positrons (antimatter counterparts of electrons). In addition, photons exist, too, as the particle equivalents of the electromagnetic field.

    When we take all the forces that we understand, i.e., not including gravity, and write down the QFT version of them, we arrive at the predictions of the Standard Model. This is where the idea of 12 fermion fields and 12 boson fields come from. These fields are excitations of the underlying theories (the Standard Model) that describe the known Universe in its entirety … all told, there are 24 unique, fundamental excitations of quantum fields possible. This is where the “24 fields” idea comes from.

  3. 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).

    There’s an intricate but ordered structure to the Standard Model, with three “generations” of particles. Why three?

    The big question, though, of why there are three generations, is driven not by theoretical motivations, but by experimental results.

    Now, there’s nothing forbidding a fourth generation from existing and being much, much heavier than any of the particles we’ve observed so far; theoretically, it’s very much allowed. But experimentally, these collider results aren’t the only thing constraining the number of generational species in the Universe; there’s another constraint: the abundance of the light elements that were created in the early stages of the Big Bang.

    … if the additional particles fit into the structure of the Standard Model as an additional generation, there are tremendous constraints. They could not have been created in great abundance during the early Universe. None of them can be less massive than 45.6 GeV/c^2. And they could not imprint an observable signature on the cosmic microwave background or in the abundance of the light elements.

  4. So are “particle” and “anti-particle” fields separate or one? In QFT, when we say “electron field,” does that denote the same field for both electron and positron?

    Ethan Siegel appears to say that “particles” and “anti-particles” occupy the same field, as excitations and reverse excitations.

    Every excitation that’s possible has a reverse excitation that’s also possible, which is why this theory implies the existence of positrons (antimatter counterparts of electrons).

    Have a particle and antiparticle annihilating? That’s described by equal-and-opposite excitations of a quantum field. Want to describe the spontaneous creation of particle-antiparticle pairs of particles? That’s also due to excitations of a quantum field.

    And this physics.stackexchange thread makes the same point: the positron field is the same as the electron field.

    All particles of the same type (e.g. photons or electrons) is understood to be ‘coming from’ one all-permeating quantum field. It should be noted that these fields also give rise to the corresponding anti-particles, so the positron field is the same as the electron field.

    So does a “particle” and its “anti-particle” occupy separate fields or the same field? My preference is one and the same – as lean a model of quanta as possible. And when they interact, it’s like destructive interference of waves.

    If I could visualize a “ripple, or excitation, or bundle-of-energy” in a field – with all the relevant properties, then maybe a “reverse” excitation would be straightforward, eh.

  5. So, how is anti-matter created on demand? And why are physicists confident that “if we were made of antimatter instead of normal matter, along with everything else on Earth, the physical and chemical properties of everything we know would remain unchanged.”

    Forbes > “Ask Ethan: Is Antimatter Sticky?” by Ethan Siegel, Senior Contributor (April 25, 2020).

    But recently, we’ve gained the ability to test out, experimentally, how antiparticles bind together. Over at CERN, the European Organization for Nuclear Research and the home of the Large Hadron Collider, an entire large complex is devoted to the creation and study of antimatter. It’s known as the antimatter factory, and its specialty involves not only producing low-energy antiprotons and low-energy positrons, but in binding them together to form anti-atoms.

  6. Regarding how to make anti-matter, this 2013 article discusses a tabletop device for creating positrons. I’ve read about devices at CERN and Lawrence Livermore, but was wondering about devices besides those at Big Science labs.

    Phys.org > “Physicists create tabletop antimatter ‘gun’” by Bob Yirka (June 25, 2013).

    An international team of physicists working at the University of Michigan has succeeded in building a tabletop antimatter “gun” capable of spewing short bursts of positrons. In their paper published in the journal Physical Review Letters, the team describes how they created the gun, what it’s capable of doing, and to what use it may be put.

    To date, the creation of positrons for study has involved very big and expensive machines. One of those is the particle accelerator at CERN. Another is a device built by scientists at Lawrence Livermore National Laboratory that created positrons by firing a hugely powerful laser at a tiny disc made of gold.

    To achieve this feat, the team fired a petawatt laser at a sample of inert helium gas. Doing so caused the creation of a stream of electrons moving at very high speed. Those electrons were directed at a very thin sheet of metal foil which caused them to smash into individual metal atoms. Those collisions resulted in a stream of electron and positron emissions – the two were then separated using magnets.

    The researchers report that each blast of their gun lasts just 30 femtoseconds, but each firing results in the production of quadrillions of positrons – a density level comparable to those produced at CERN. [How is that particle density counted? Can the positrons be trapped for various experiments?]

  7. So, a sort of chicken-or-the-egg question about quantum fields.

    • Forbes > “Ask Ethan: When Did The Universe Get Its First Quantum Fields?” by Ethan Siegel, Senior Contributor (Oct 9, 2020) – Is there a time where the Universe didn’t have the same quantum fields?

    [Contrary to visualization of classical fields], a quantum field isn’t only present where you have a source (like a mass or a charge), but rather is omnipresent: everywhere.

    If you have charges present, such as:

    • masses (for gravity),
    • electric charges (for electromagnetism),
    • a particle with a nonzero weak hypercharge (for the weak nuclear force),
    • or a color charge (for the strong nuclear force),

    they behave like an excited state of the field, but the field is present regardless of the presence or absence of charges. What’s more: the field is quantized, and its zero-point energy, or the lowest energy level it can occupy, is allowed to have non-zero values.

    In other words, “empty space” as we understand it, with no charges, masses, or other sources of the field in it, isn’t exactly empty, but still has these quantum fields present within it.

    Siegel discusses evidence and speculation. Evidence like the Casimir effect and patterns in the CMB. Speculation on whether the fields of the Standard Model are all inclusive (and “the running of the coupling constants” in cosmic evolution of the Big Bang), possible variations in symmetry breaking after an initial state of unification, and models of cosmic inflation.

    He concludes:

    However, one thing that is certain is that quantum fields of some variety must have still existed during inflation. … How do we know? Because the fluctuations that we see in the Universe, the ones that gave rise to the cosmic structure that eventually formed, match exactly the ones predicted to arise from fluctuating quantum fields that existed during inflation.

    For as long as spacetime has existed, some version of quantum fields must have existed as well.

    Entangled verse

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