Formalism keyword	Formalism description
'sphten−liouv'	Liouville space formalism: the fundamental operators from which the basis set is built are single‐spin irreducible spherical tensors. These operators are ordered with respect to many common transformations and conservation laws encountered in magnetic resonance. Many operations may therefore be performed semi‐analytically. A lot of Spinach functionality either requires this formalism or operates most efficiently within it.
'zeeman−liouv'	Liouville space formalism: the fundamental operators from which the basis set is built are single transition operators between the projection states onto the Z axis. The state vector coefficients in this formalism are easy to interpret because they correspond to populations of standard textbook spin states. This formalism is essentially a vectorisation of 'zeeman−hilb'; it permits only limited state space reduction; most calculations would have exponential complexity scaling if this option is chosen.
'zeeman−hilb'	Hilbert space formalism: the fundamental states from which the basis set is built are the projection states onto the Z axis. This is the standard density operator formalism described in most magnetic resonance textbooks. Only the core functionality (operators, states, propagators, and evolution) is available. This option is mostly useful for backwards compatibility checks; it cannot support complicated relaxation theories or chemical kinetics. All calculations within this formalism would have exponential complexity scaling.