Last updated July 23, 2024

Quantum field theory

Description of the image: This representation of the molecular wave function shows the boundary of atoms in a molecule. Where does an atom begin and end? The atom is a field, and it is the field lines that define its volume. No one has ever seen the fields of quantum physics, but it might look like this computer image. When atoms bond together, their fields distort; this distortion characterizes the bonds. Particles in quantum theory are not "little balls" but undulations, fields that possess a wavelength. This wavelength represents the size of the particle, and the field, the energy of the particle. Image credit: T.A. Keith.

The Fields of Reality

When discussing matter and its behavior in the infinitely small world of particles, we address quantum field theory. Quantum field theory helps us understand particle physics. In certain situations, the number of particles entering a portion of spacetime fluctuates and differs from the number exiting.
The number of particles changes when, for example, an atom in an initial state yields an atom plus one photon in a final state. In other words, a photon suddenly emerges from the vacuum and appears in the electromagnetic field. Quantum theory tells us that in the real world, everything is a "field."
We are entirely immersed, down to our deepest selves, in multiple fields with astonishing characteristics. The field is a fundamental concept in physics; it consists of nothing else, yet it constitutes the real world. Fields carry the energy of everything that exists in the universe, from atoms to large galactic structures.
Magnetism, gravity, nuclear force, light, matter, and many other physical phenomena are carried by fields. The most surprising aspect is that matter itself, the substance we are made of, consists of a set of fields. Electrons and protons are also fields, thus we are made of fields that defy intuition.
In other words, we are made of an aggregate of ghostly quantum particles bathing in fields. These fields carry the energy of the particles throughout all available space around them.

With the notion of a field, the vision of the nature of things is astonishing; reality becomes strange and eludes our five main senses. Reality is not simply explained by the presence of matter but also by the exchanges and interactions between real objects and the virtual objects of low-energy quantum fields.
In the quantum world, all particles of the standard model, fermions, and bosons, emerge from vibrations in a field. This is the basic concept of how particle accelerators like the Large Hadron Collider (LHC) work. When scientists want to observe a particle, they provoke collisions whose energy corresponds to the particle in question.
Quarks and electrons constitute ordinary matter, whereas matter above absolute zero (-273.15 °C) emits radiation, i.e., light that travels in a field. Each type of fermion and each type of boson has its own field. Particles are considered excited states of these fields.
The "wave-particle duality" of light was extended to electrons in 1929 by the French mathematician and physicist Louis de Broglie (1892−1987), and then to all particles. However, our mind needs an image of our world to feed its intuition and represent concepts.
But conceptualizing quantum theory and all the quantum fields in which we exist is not easy. Everything is "field," yet quantum fields, which are dynamic, bubbling, and charged systems, are all subsets of the gravitational field or the electromagnetic field, the only two fundamental fields of nature.

Description of the image: A field cannot be represented by an image, but it can be mapped.

What is a Field?

In physics, a field is three things linked in a system with a large number of objects. A delimited portion of space, a measurable physical quantity, and a relationship that links the portion of space to the physical quantity. In other words, a field is filled with physical quantities, measurable objects quantifiable with an instrument, where each point in the portion of space is linked to the physical quantity by a correspondence or function. For example, atmospheric pressure, air temperature, wind speed, but also rain, magnetism, gravity, radioactivity, can be represented by fields.

Fields are scalar or vector.
A scalar field is measurable by a single quantity. For example, temperature or mass is defined by a physical quantity, entirely measurable by a single value.
A vector field is associated with a vector quantity, that is, a quantity for which a single value is not sufficient. An orientation is also needed, that is, a direction and a sense, as in a wind speed field.

How to represent a field?
For a scalar field, it is enough to represent the areas where the value is identical, as in a field of temperatures or pressures (see 1st and 3rd thumbnails).
For a vector field, it is enough to represent the field lines where each point is a tangent field vector, as in the wind direction field or in a magnetic field (see 2nd and 4th thumbnails).
The energy of the field fades in space. This is why, outside the electromagnetic field generated by a radio station, one does not receive anything at all. When an electromagnetic field is suddenly interrupted, a spark occurs (the field indeed contains energy).

And the quantum field?
In quantum physics, the notion of corpuscle is not used since quantum particles are not corpuscles but mathematical quantities represented by state vectors in Hilbert space. This concept escapes intuition and our vision.

The quantum field fills all space. It is a vector field of subatomic particles, whose quantity is quantized (taken in a finite set of values) and the relationship is a wave function (state vector). This allows knowing all the information of the system and gives every particle the typical interference properties of a wave.
In the quantum world, all particles in the ground state (non-excited) are waves.
A hadron field consists of virtual particles, partons (gluons and quarks) that agitate, appearing and disappearing in empty space.
A field carried by the weak nuclear force is traversed by W and Z bosons.
An electromagnetic field is traversed by photons.
A gravitational field is traversed by "gravitons" (not yet discovered) because gravity is a very weak force.
Thus, the virtual and real particles of matter bathe in these bubbling fields, occasionally transferring their energy. This is what scientists provoke in a collider. In a collider, when an electron and a positron meet, they annihilate and transfer their energy to the vacuum's turmoil. This energy creates real material particles that emerge from the vacuum and appear for a few "moments" on computer screens.

A field is thus a bubbling system occupying all space, an undulation, a vibration, an oscillation, a wave that has a wavelength and thus a frequency.
Thanks to Max Planck's formula e=hν (1858−1947), a field also has energy (e is the energy of something moving, h is Planck's constant, and ν, the Greek letter nu, the frequency). This pair of values, energy and frequency, characterizes the field at every point in space. Every point in space allows the emergence or annihilation of particles.

Quantum field theory

The Fields of Reality

What is a Field?

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