Abstract
We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum mechanical system along a closed loop of parameter space may yield a geometric mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization one obtains, in addition, a Schwinger term. Depending on the type of transformation a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space. (authors).
Grosse, H;
[1]
Langmann, E
[2]
- Vienna Univ. (Austria). Inst. fuer Theoretische Physik
- Technische Univ., Graz (Austria). Inst. fuer Theoretische Physik und Reaktorphysik
Citation Formats
Grosse, H, and Langmann, E.
The geometric phase and the Schwinger term in some models.
Austria: N. p.,
1991.
Web.
Grosse, H, & Langmann, E.
The geometric phase and the Schwinger term in some models.
Austria.
Grosse, H, and Langmann, E.
1991.
"The geometric phase and the Schwinger term in some models."
Austria.
@misc{etde_10139925,
title = {The geometric phase and the Schwinger term in some models}
author = {Grosse, H, and Langmann, E}
abstractNote = {We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum mechanical system along a closed loop of parameter space may yield a geometric mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization one obtains, in addition, a Schwinger term. Depending on the type of transformation a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space. (authors).}
place = {Austria}
year = {1991}
month = {Dec}
}
title = {The geometric phase and the Schwinger term in some models}
author = {Grosse, H, and Langmann, E}
abstractNote = {We discuss quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfill an algebra of charges with Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum mechanical system along a closed loop of parameter space may yield a geometric mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization one obtains, in addition, a Schwinger term. Depending on the type of transformation a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space. (authors).}
place = {Austria}
year = {1991}
month = {Dec}
}