Quantum Fields Forever

What is a quantum field and how does it interact with matter? 

Answer by Viktor T. Toth, IT pro, part-time physicist, on Quora:

Quantum fields are the quantum-theoretical generalizations of classical fields. The two archetypal classical fields are Maxwell’s electromagnetic field and Einstein’s metric field of gravitation. One way to think about the process of quantization is that we first reformulate the (still classical) field equations in terms of mathematical operators replacing some numerical quantities (this part is pure algebra/calculus, no new physics is introduced yet); but then, we “solve” the resulting operator-valued equations, including solutions that do not appear in the classical theory, and make the assertion (validated by observation) that these new, “nonsensical” (in an intuitive, not in a mathematical sense) solutions accurately describe Nature, including all the observed quantum behaviour that contradict the classical theory.

There are several rationales for using quantum field theory. First, it is a natural generalization of classical field theories, which are our most successful (non-quantum) theories of Nature. Second, a quantum field theory can account for the (observed, well-studied) creation and annihilation of particles, processes that do not exist in quantum mechanics. Third, quantum field theory is inherently relativistic, and “magically” (not really, just elegant math) resolves issues of causality that plague even relativistic quantum particle theories.

But no, quantum fields do not interact with matter. Quantum fields are matter. In quantum field theory, what we perceive as particles are excitations of the quantum field itself.

The simplest “practical” quantum field theory is quantum electromagnetism. In it, two fields exist: the electromagnetic field and the “electron field”. These two fields continuously interact with each other, energy and momentum are transferred, and excitations are created or destroyed. So for instance, what we picture intuitively as an electron absorbing a photon is, in quantum electrodynamics, a specific interaction between the electromagnetic field and the electron field, in which the electromagnetic field loses one excitation quantum, and the electron field gains its energy, momentum and angular momentum.

Quantum Fields (Real or Not)

(Last Updated On: October 12, 2019)

Field

Before getting into quantum field lets first talk about the field, so a field is any quantity that measures pretty much all the points in space and now this quantity could be a scalar quantity like electric potential or a vector quantity including tensors. If we talk about an electromagnetic field. it’s made up of two fields, an electric field, and a magnetic field or in simpler words, we can say that we UNIFY them.

Quantum Field

likewise, a quantum field is a Quantum measurement assigned to every point in space. If we step down from an electromagnetic field to an energy field. Quantum properties are intertwined with each other through a wave function and if we imagine the quantum properties to be a part of fundamental fields, then they no longer would be attached to the particles.

There are a total of 17 different elementary particles with unique properties and they are as mentioned below –

Elementary Particles

Some of those properties are fixed and others are unpredictable like spin orientation etc, we’ll be needing around hundreds of fields if we start treating these properties as a field but we might group them together as we did with the electromagnetic field. The basic quantum numbers we have are the spin, electric charge and colour change. we can distinguish gluons from photons on the basis of colour change. so if we make groups using such a strategy so we get 37 fields instead of hundreds of fields, we’ve got six Leptons, 6 Quarks each with 3 possible colour-charges, 8 colour charge distribution for gluons, 1 photon, 3-week Bosons, and 1 Higgs.

The existence of the field everywhere in space-time doesn’t mean that the particles are everywhere. We only get a particle when the Quantum field gets excited.

Quantum field theory model tells us how the quantum field interacts, so a quantum field is a set of quantum properties assigned to every point in space and each of them existing alongside with others, allowing them to interact and any energy in a field higher than it’s vacuum state will be seen as a particle carrying the properties of that field just as our physical reality is described by the Quantum field theory, these complex systems are more than just the combinations of these fields put together into some stable or quasi-stable bound state.

We can consider this entire universe to be a complicated quantum field, that holds the entire physics. Quantum fields can describe an arbitrarily large number of particles that interact in all ways our theories can conceivably allow. and they do this not in some vacuum of empty space but amidst a background of not so empty space which plays by the rules of quantum field theory too. As we know that particles, Anti-particles and all sort of excitations of the fields are constantly being created and destroyed where the reality must be fundamentally different from the classical picture of a smooth, continuous and a well-defined Universe where the Theory of everything is even much more complicated, and this remains an unsolved problem.