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Canonical Coherent States

S. Twareque Ali, Jean-Pierre Antoine, Jean‐Pierre Gazeau

Theoretical and mathematical physicsAug 26, 20130 citations

Covariance and uniqueness of the canonical fermion coherent state

Chang Jae Lee

A unitary Fock-space operator that leaves the canonical quantization rule for fermions covariant is introduced. The defining equation of a canonical fermion coherent state retains the symmetry under this unitary transformation. This fact mandates that the coherent state must accompany a partner state, and that the form of a state in the pair is related to the partner state by the symmetry. A careful definition of the phase in the extended fermion Fock space is crucial for the uniqueness of the normalized fermion coherent state. Also the proper choice of the phase renders the canonical fermion coherent state equal to a displaced-vacuum state.A unitary Fock-space operator that leaves the canonical quantization rule for fermions covariant is introduced. The defining equation of a canonical fermion coherent state retains the symmetry under this unitary transformation. This fact mandates that the coherent state must accompany a partner state, and that the form of a state in the pair is related to the partner state by the symmetry. A careful definition of the phase in the extended fermion Fock space is crucial for the uniqueness of the normalized fermion coherent state. Also the proper choice of the phase renders the canonical fermion coherent state equal to a displaced-vacuum state.

Physical Review ANov 1, 19922 citations

Canonical coherent states for the relativistic harmonic oscillator

V. Aldaya, Julio Guerrero

In this paper there are constructed manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given SL(2,R) representation, once a change of variables z∈C→zD∈ unit disk is performed. Also introduced are higher-order, relativistic creation and annihilation operators, â,â°, with canonical commutation relation [â, â°]=1 rather than the covariant one [ẑ, ẑ°]≊ energy and naturally associated with the SL(2,R) group. The canonical (relativistic) coherent states are then defined as eigenstates of â. Finally, a canonical, minimal representation is constructed in configuration space by means of eigenstates of a canonical position operator.In this paper there are constructed manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given SL(2,R) representation, once a change of variables z∈C→zD∈ unit disk is performed. Also introduced are higher-order, relativistic creation and annihilation operators, â,â°, with canonical commutation relation [â, â°]=1 rather than the covariant one [ẑ, ẑ°]≊ energy and naturally associated with the SL(2,R) group. The canonical (relativistic) coherent states are then defined as eigenstates of â. Finally, a canonical, minimal representation is constructed in configuration space by means of eigenstates of a canonical position operator.

arXiv:hep-th/9406080Journal of Mathematical PhysicsJul 1, 199512 citations

Generalized coherent states

A. D. Jannussis, G. Karayannis, Παναγιώτης Παναγόπουλος +1 more

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoOct 1, 19834 citations

Strong convergence of a resolution of the identity via canonical coherent states

Ryo Namiki

A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with the framework of the spectral theorem. We provide an elementary proof of the strong convergence for the resolution of the identity due to canonical coherent states starting with a mostly familiar setup. Further, we enjoy a different proof and show that the relevant uniform limit does not exist.A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with the framework of the spectral theorem. We provide an elementary proof of the strong convergence for the resolution of the identity due to canonical coherent states starting with a mostly familiar setup. Further, we enjoy a different proof and show that the relevant uniform limit does not exist.

arXiv:2402.08317Feb 13, 20240 citations

Generalized Coherent States

Thalanayar S. Santhanam

Springer eBooksJan 1, 19802 citations

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