CCR algebra

The CCR layer implements symbolic bosonic operator algebra on top of the core term objects. Instead of forming matrix representations, it rewrites operator words into normally ordered expansions using commutation relations.

At this layer, Symop works with three closely related symbolic objects:

• operator polynomials, represented by symop.ccr.algebra.op.poly.OpPoly

• ket polynomials, represented by symop.ccr.algebra.ket.poly.KetPoly

• density polynomials, represented by symop.ccr.algebra.density.poly.DensityPoly

The main ideas are:

• operator words are expanded symbolically using CCR normal ordering

• kets are finite sums of normally ordered monomials

• density operators are finite sums of outer products \(|L\rangle\langle R|\)

• actions, products, traces, and inner products are all computed symbolically

• Ket algebra
• Density algebra
• Operator algebra
• Normal ordering, expectation values, and trace