Quantum Field Theory

In QFT all particles are considered as “excitations” that form from the underlying fields of physical reality. In essence, particles — the base “material” of physical reality — emerge from a nonphysical source.

Paul Dirac, a British mathematician and physicist, laid the foundations of Quantum Field Theory in the 1920’s with the composition of his famous equation — the Dirac Equation — which describes the behaviour of relativistic electrons. The Dirac Equation also describes the behaviour of the majority of other matter particles in addition to electrons.

Standard Quantum Theory was developed in the 1920’s by Werner Heisenberg and Niels Bohr. Standard Quantum Theory is accurate for describing the behaviour of singular particles in isolation, when they are moving at moderate speeds. The issue, however, is that reality doesn’t generally do isolation, and particles don’t often exist in isolation.

Moreover, in the universe particles are moving much faster — near the speed of light — and the complexity with which they interact with one another requires new, more advanced, physics, theories, and maths to accurately describe.

The Development of Quantum Field Theory

Quantum field theory developed beginning in the 1920’s, although technically, the revolutions of mathematical physics such as the work of Isaac Newton in the 17th century can be considered its earliest direct roots since Newton’s Law of Universal Gravitation was the first successful classical field theory.

The development of QFT began in the 1920s with the description of interactions between light and electrons. [2] The result of this description was quantum electrodynamics — the first quantum field theory. [2]

Major theoretical obstacles arose with the emergence of quantum electrodynamics. First it was a number of infinities. Various infinities appearance in perturbative calculations, [2] which to this day have not been delt with. One such infinity is the infinite energy density of the vacuum, the infinite energy in the space all around us.

These infinities were dealt with in the 1950s with the invention of renormalization procedure. [2] However this isn’t actually a solution, but a reduction of the problem, a way to void it without actually resolving it.

A second major obstacle arose with QFT’s inability to describe the strong interaction and the weak interaction (of the strong force and the weak force). [2]

This obstacle was so severe that a fraction of theorists believed the field theory approach would have to be abandoned. [2] It wasn’t until the development of gauge theory and the completion of the Standard Model in the 1970s that a new era of QFT began. [2]

Notes

• Quantum field theory is the result, and built on the foundations of, classical field theory, special relativity, and quantum mechanics developed throughout the 20th century. QFT is a theoretical framework as part of theoretical physics.
• QFT is used in particle physics to construct physical models of subatomic particles, and is used in condensed matter physics to construct models of quasiparticles. [2]
• The standard model of particle physics is based on QFT. [2]
• The equation of motion of a particle is determined by minimization of the action computer for the Lagrangian, which is a function of fields associated with the particle. [2]
• Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. [2]
• Each interaction can be represented by a Feynman diagram according to perturbation theory in quantum mechanics. [2]
• QFT development began in the 1920’s with the description of interactions between light and electrons, which resulted in the first QFT — quantum electrodynamics. [2]

Resources

1. Rutherford, Michael. (year). Quantum Mechanics For Beginners, p. 52.
2. Wikipedia Editors. Quantum Field Theory. Wikipedia. <https://en.wikipedia.org/wiki/Quantum_field_theory>. Accessed 20 Dec 2024.