TY - CHAP

T1 - Inequalities expressing the Pauli principle for generalized observables

AU - Werner, R. F.

PY - 1989

Y1 - 1989

N2 - We define the second quantization of generalized observables, i.e. observables described by positive operator valued rather than projection valued measures. Given any such observable in the one-particle Hilbert space, this procedure yields a generalized observable in a many-particle system of Bosons or Fermions. This generalization of the usual construction is used to define obervables corresponding to the density of systems in one-particle phase space (i.e. a Boltzmann density), from the (never projection valued) observables localizing a particle in phase space. In this framework the Pauli principle takes the form of an inequality for the distribution of the particle number in a given region in phase space. Arbitrarily high occupation numbers may occur, but the probability of finding more than one particle per normalized phase space volume decreases very rapidly.

AB - We define the second quantization of generalized observables, i.e. observables described by positive operator valued rather than projection valued measures. Given any such observable in the one-particle Hilbert space, this procedure yields a generalized observable in a many-particle system of Bosons or Fermions. This generalization of the usual construction is used to define obervables corresponding to the density of systems in one-particle phase space (i.e. a Boltzmann density), from the (never projection valued) observables localizing a particle in phase space. In this framework the Pauli principle takes the form of an inequality for the distribution of the particle number in a given region in phase space. Arbitrarily high occupation numbers may occur, but the probability of finding more than one particle per normalized phase space volume decreases very rapidly.

M3 - Contribution to book/anthology

VL - 1

T3 - Leuven Notes Math. Theoret. Phys. Ser. A Math. Phys.

SP - 179

EP - 196

BT - Mathematical methods in statistical mechanics (Leuven, 1988)

A2 - Fannes, Mark

A2 - Verbeure, André

CY - Leuven

ER -