triqs_tprf::product

#include <tprf/linalg.hpp>

Synopsis

template<Channel_t CH>
g2_iw_t product (g2_iw_cvt A, g2_iw_cvt B)

Two-particle response-function product \(A * B\)

The two-particle response functions \(A \equiv A_{abcd}(\omega, \nu, \nu')\) and \(B \equiv B_{abcd}(\omega, \nu, \nu')\) are cast to matrix form and their product is computed

\[(A * B)_{\{\nu\alpha\beta\}, \{\nu'\gamma\delta\}}(\omega) = \sum_{\bar{\nu}ab} A_{\{\nu\alpha\beta\}, \{\bar{\nu}ab\}}(\omega) B_{\{\bar{\nu}ab\}, \{\nu'\gamma\delta\}}(\omega)\]

where the mapping of target-space indices \(\{a, b, c, d \}\) to \(\{\alpha, \beta\}, \{\gamma, \delta\}\) is channel dependent.

Storage is allocated and the product is returned by value.

Template parameters

  • CH selects the two-particle channel

Parameters

  • A two-particle response function \(A \equiv A_{abcd}(\omega, \nu, \nu')\)

  • B two-particle response function \(B \equiv A_{abcd}(\omega, \nu, \nu')\)

Returns

\((A * B)\) in the given channel