Encodings
LadderOperatorSequence Module
Normal ordering of fermionic operator products.
A product of ladder operators a†₂ a₀ a†₁ a₃ is in normal order when all creation operators (a†) are to the left of all annihilation operators (a). Reordering requires swapping adjacent operators. Each swap of two fermionic operators introduces a factor of −1 (from the CAR), and swapping a†ᵢ past aᵢ (same index) generates a δᵢⱼ term. The ConstructNormalOrdered function performs this reordering, tracking all signs and generated terms, producing an S type (sum of products).
Types
| Type | Description |
|
A sum expression of ladder operators parameterized by a combining algebra (e.g., fermionic anti-commutation relations). |
Functions and values
| Function or value |
Description
|
Full Usage:
toIndexOrder productTerm
Parameters:
P<IxOp<uint32, LadderOperatorUnit>>
-
The product term containing ladder operators to sort.
Returns: P<IxOp<uint32, LadderOperatorUnit>>
A new product term with raise operators sorted ascending and lower operators descending by index, with phase adjusted for swaps.
|
Sorts the raise and lower operators within a product term into index order. Uses a selection sort that tracks sign changes from swaps. Raise operators are sorted in ascending order by index, while lower operators are sorted in descending order by index.
|