Quantum Field Theory

Quantum Field Theory is the

Theoretical Background

Quantum Electrodynamics (QED)

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The Development of Quantum Field Theory began with study of electromagnetic interactions, because during the 1920s the only known classical fields were the electromagnetic field and the gravitational field.

A quantum theory of the free electromagnetic field — considering the electromagnetic field alone by excluding interactions between particles and the field — was developed in the works of Born, Heisenberg, and Pascual Jordan in 1925–26. [1]

This quantum theory was developed using canonical quantization, treating the electromagnetic field as a set of quantum harmonic oscillators. [1] However, because this theoretical framework excluding matter interactions in its development, its usefulness was limited as it couldn’t be applied to the real world, and could therefore not make predictions on physical interactions.

In Paul Dirac’s seminal paper The quantum theory of the emission and absorption of radiation (1927) coined the term Quantum Electrodynamics. In QED Dirac added terms for the electric current density and the electromagnetic vector potential on top of the terms describing the free electromagnetic field. [1]

Using first-order perturbation theory he was able to successfully explain the phenomenon of spontaneous emission. [1] According to quantum mechanics’ uncertainty principle, quantum harmonic oscillators cannot remain stationary — even at absolute zero. Quantum harmonic oscillators have a non-zero minimum energy, even at their lowest energy state (ground state), and thus must always be oscillating. [1] Thus even in a perfect vacuum, at absolute zero, an oscillating electromagnetic field having zero-point energy exists. [1]

It is the ground state quantum fluctuations of electromagnetic fields in a vacuum (zero-point energy) that “results in “stimulates” spontaneous emissions of photons from electrons in the vacuum. [1]

Dirac’s theory was “hugely successful” for explaining emission and absorption of photons by atoms. [1] By applying second-order perturbation theory, Dirac’s theory was able to account for the scattering of photons, resonance fluorescence, and non-relativistic Compton scattering. [1]

However, even with the success of this development, infinities in calculations continued to cause problems in the application of higher-order perturbation theory in the development of quantum field theory.