Computing the magnetic field response of the proton.

Background field methods offer an approach through which fundamental non-perturbative hadronic properties can be studied. Lattice QCD is the only ab initio method with which Quantum Chromodynamics can be studied at low energies; it involves numerically calculating expectation values in the path integral formalism. This requires substantial investment in high performance supercomputing resources. A particular challenge of lattice QCD is isolating the desired state, rather than a superposition of excited states. While extensive work has been performed which allows the ground state to be identified in lattice QCD calculations, this remains a challenging proposition for the ground state in the presence of a uniform magnetic field field. Quark level projection operators are introduced to resolve this challenge and thus allow for extraction of the magnetic polarisability. [ABSTRACT FROM AUTHOR]