| 研究実績の概要 |
The methods of effective field theory (EFT) construction from relativistic theories were extended to develop a new EFT that is able to describe a non-relativistic system - a solid. This relied on a technique for constructing a non-relativistic EFT from a fully relativistic EFT, treating the former as spontaneously breaking (some of) the symmetries of the latter. This technique was developed so as to deal with additional internal symmetries. The system described is a two-component solid, and redundancies between allowed operators resolved. A physical system that realises this symmetry breaking pattern was identified, namely bi-layer graphene (which recently has been under study due in connection with 'magic angle superconductivity). The resulting low-energy EFT is that of acoustic phonons along with what this work dubbed 'pseudo-acoustic' phonons. Already the potential application of this system to dark matter direct detection was highlighted; the interaction of pseudo-acoustic phonons could raise the scattering rate of dark matter by better satisfying energy-momentum conservation requirements.
The use of spinor helicity variables and their geometry was further elucidated, resulting in a novel way of describing the manifold upon which all possible particle interactions occur. This achieved a 'geometrizing' of observables in scattering experiments.
The mathematical machinery of Hilbert series, which solved a number of redundancy problems in EFT construction, was further developed by studying asymptotic formulae (corresponding to a high-temperature limit of the free theory).
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