Seminar Series

Fierz reformulation of the Einstein-Dirac Equations


Peter Jarvis


University of Tasmania

Time & Place

Fri, 12 May 2017 11:00:00 NZST in Rutherford 531, Level 5

All are welcome


Understanding classical solutions to relativistic field equations has provided fundamental new insights into physical phenomena as diverse as instantons, magnetic monopoles, the Higgs mechanism, and the inflationary universe. Coupled systems are notoriously difficult, and there is for example precious little information on the Maxwell-Dirac, or Einstein-Dirac systems (electromagnetism, or gravity, interacting with a charged or massive spin -½ field, respectively). In this talk we report on how to transcribe the Einstein-Dirac equations into a new set of variables, with parametrize the relativistic equivalent of the usual Bloch vector, rather than the spinor wave-function. Remarkably, the relevant quantities, the so called Fierz currents, which are bilinear in the spinor wavefunction, also provide the ingredients of a vierbein field (local Lorentz frame), which is at the same time enough to specify the space-time metric. In this way the Einstein-Dirac equations are ‘geometrized’ in the sense that as well as the curvature on the left-hand side of the equations, the matter contribution on the right-hand side – the energy-momentum tensor of the Dirac field – is also a function of the vierbein itself, though its identification with the Fierz currents. The talk will walk through some of the motivation, context and antecedents for carrying out these steps, as well as giving a brief technical overview on progress to date. Joint work with Shaun Inglis