Positive Quantization in the Presence of a Variable Magnetic Field

Marius Mantoiu (1, 2) , Radu Purice (2) , Serge Richard (3)

1 Departamento de Matematicas
2 IMAR - "Simion Stoilow" Institute of Mathematics
3 PSPM - Probabilités, statistique, physique mathématique

Starting with a previously constructed family of coherent states, we introduce the Berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural Poisson algebra. The phase-space reinterpretation involves a magnetic version of the Bargmann space and leads naturally to Berezin-Toeplitz operators.

Domaines: Physique mathématique [math-ph]

Marius Mantoiu, Radu Purice, Serge Richard. Positive Quantization in the Presence of a Variable Magnetic Field. Journal of Mathematical Physics, 2011, 52 (11), pp.112101. ⟨10.1063/1.3656253⟩. ⟨hal-00660880⟩