Fermionic Coherent

An extension of the notions of bosonic coherent state and fermionic coherent state . A k-fermionic coherent state is a linear combination of the eigenvectors of a generalized number operator N, a generator of a k-fermionic algebra {f ₋, f ₊, f ₊ ⁺, f ₋ ⁺, N}, with coefficients in a Grassmann algebra . Such a state is an eigenvector of an annihilation operator (f ₋ or f ₊ ⁺). The k-fermionic algebra {f ₋, f ₊, f ₊ ⁺, f ₋ ⁺, N}, with k ∈ N\{0, 1 }, results from the combination of a q-uon algebra {f ₋, f ₊, N} and a q¯-uon algebra {f ₊ ⁺, f ₋ ⁺, N} with q : = exp(2πi/k) and qq¯ = 1. The q-uon algebra and the q¯-uon algebra do not commute except in the cases k = 2 and k → ∞ for which they coincide (f ₋ ≡ f ₊ ⁺ and f ₊ ≡ f ₋ ⁺). Therefore, the k-fermionic coherent state is an ordinary fermionic coherent state for k = 2 and an ordinary bosonic coherent state for k→ ∞. A coherence factor, that generalizes the coherence factor used in quantum optics, can be defined from the expectation...