An obstruction to quantization of the sphere

TY - JOUR

T1 - An obstruction to quantization of the sphere

AU - Hawkins, Eli

PY - 2008/11

Y1 - 2008/11

N2 - In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter h is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S2) in which h can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing S2 is never connected.

AB - In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter h is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S2) in which h can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing S2 is never connected.

KW - Mathematical Physics

UR - http://www.scopus.com/inward/record.url?scp=50249171135&partnerID=8YFLogxK

U2 - 10.1007/s00220-008-0517-2

DO - 10.1007/s00220-008-0517-2

M3 - Article

SN - 0010-3616

VL - 283

SP - 675

EP - 699

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -