Using field theory to understand material reality

Prof James Binney FRS

The Vacuum Comes Alive

Podcast Presentation (PDF)

For Newton gravity was action at a distance. During the 18th century the concept of a field was introduced to facilitate the computation of forces. With Faraday's work on magnetism, a field emerged as something physical. The reality of fields was put beyond doubt by Maxwell's interpretation of an electromagnetic wave as a system in which an E field generated a B field, which regenerated the E field, all in the absence of charges. In the middle of the 20th century it became clear that the vacuum (aether) is a complex dynamical system that supports several fields, including the EM field. A Lagrangian L is a simple function that encodes the vacuum's dynamics. Each field contributes a section to L, and other terms specify how the fields are coupled together. The forms of all terms are strongly constrained by the requirement for Lorentz invariance.

Dr Joseph Conlon

Matter Emerges from the Vacuum

Podcast Presentation (PDF)

This talk discusses the quantisation of classical fields leads to a picture of quantum fields as an infinite number of harmonic oscillators. In this picture, the vacuum corresponds to being in the ground state of all these oscillator, and particles are interpreted as excited states of these oscillators.

Prof Fabian Essler

Making the Vacuum Concrete

Podcast Presentation (PDF)

Quantum Mechanics arises from relativistic Quantum Field Theory in a special limit. This talk shows that the reverse can occur as well - Quantum Field Theory can arise in a limit of non-relativistic quantum many-particle systems. The talk first considers the quantum theory of lattice vibrations in solids and show that the physics at long wavelengths is described by the Klein-Gordon QFT. This shows how QFT can “emerge” at length scales that are large compared to a characteristic microscopic scale, which for example of lattice vibrations is simply the lattice constant. This simple example provides a very nice perspective for thinking about QFT in general, and the vacuum state in QFT in particular. The final part of the talk considers the non-relativistic quantum theory of electronic degrees of freedom in certain anisotropic solids, and show how this gives rise to an emergent QFT exhibiting quantum number fractionalization.