gamma

gamma(mode, is_prime)

Create a majorana fermion.

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For a given mode i, two majorana fermions can be created:

• gamma(i, False) creates $\gamma = a_i^\dagger + a_i$
• gamma(i, True) creates $\gamma' = i(a_i^\dagger - a_i)$

The argument order is (mode, is_prime) to reflect the natural interpretation of majorana operators: first specify the mode, then the variant. Unlike fermionic operators – where the distinction between creation and annihilation is fundamental – the two majorana variants are more symmetric and conceptually less different.

This mirrors the normal-ordering convention for majoranas, where operators are sorted first by mode and then by variant. For example, a normally ordered string like ((1, True), (0, False), (0, True) is more readable and intuitive than ((True, 1), (False, 0), (True, 0).

Parameters

• mode (int) – index of the fermionic mode.
• is_prime (bool) – whether to create $\gamma$ (False) or $\gamma'$ (True).

Returns

A MajoranaAction object, which is essentially the flat index 2*mode+int(is_prime).

Return type

int