Function sequant::mbpt::bernoulli::detail::nested_commutator_coefficients¶

Function Documentation¶

container::svector<PartitionPathCoefficients> sequant::mbpt::bernoulli::detail::nested_commutator_coefficients(std::size_t max_order)¶

Generates the partition paths and exact rational coefficients of every homogeneous Bernoulli contribution through max_order.

For \(b_n\) defined by

\[ \frac{x}{\exp(x)-1} = \sum_{n=0}^{\infty} b_n x^n, \]

this applies Eq. (44) of 10.1063/1.5030344 in the form

\[ V_m = (-1)^m b_m \operatorname{ad}_{\sigma}^{m}(V) - \sum_{j=1}^{m} b_j \operatorname{ad}_{\sigma}^{j}((V_{m-j})_R). \]

Duplicate paths are combined exactly, zero coefficients are removed, and pairs related by \(A-R=N\) are represented by the corresponding N path.