Details
| Original language | English |
|---|---|
| Title of host publication | Mathematical methods in statistical mechanics (Leuven, 1988) |
| Editors | Mark Fannes, André Verbeure |
| Place of Publication | Leuven |
| Pages | 179-196 |
| Number of pages | 18 |
| Volume | 1 |
| Publication status | Published - 1989 |
Publication series
| Name | Leuven Notes Math. Theoret. Phys. Ser. A Math. Phys. |
|---|---|
| Publisher | Leuven Univ. Press |
Abstract
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Mathematical methods in statistical mechanics (Leuven, 1988). ed. / Mark Fannes; André Verbeure. Vol. 1 Leuven, 1989. p. 179-196 (Leuven Notes Math. Theoret. Phys. Ser. A Math. Phys.).
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
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 -