Equal-Time Commutation Relations of the Isovector Current Densities
- 25 August 1967
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 160 (5), 1366-1374
- https://doi.org/10.1103/physrev.160.1366
Abstract
The one-particle matrix elements of the local equal-time commutators of the isovector currents are derived by applying the Dyson representation to the causal parts of the invariant absorptive parts. Assuming the equal-time commutation relation between the total charge and charge density and also assuming certain asymptotic limits for the Dyson spectral function, we can generate the local equal-time commutation relations between various components of the currents. It is shown that, for a reasonable asymptotic behavior of the spectral function, the charge-space component has no antisymmetric (in isospin) Schwinger terms, but involves two possible -numer symmetric Schwinger terms, and that the space-space components can have no antisymmetric Schwinger terms. It is pointed out that as the asymptotic behavior becomes worse, we can no longer define the equal-time commutation relations uniquely.
Keywords
This publication has 11 references indexed in Scilit:
- Sum Rules Based on CausalityPhysical Review Letters, 1967
- Gauge Invariance, Lorentz Covariance, and Current Correlation FunctionsPhysical Review B, 1966
- Necessity of Additional Unitary-Antisymmetric-Number Terms in the Commutators of Spatial Current ComponentsPhysical Review B, 1966
- Applications of the ChiralAlgebra of Current DensitiesPhysical Review B, 1966
- Current commutation relations in the framework of general quantum field theoryCommunications in Mathematical Physics, 1966
- Currents and sum rules in vector-meson theoryIl Nuovo Cimento A (1971-1996), 1966
- Equal-time commutators and dispersion relationsIl Nuovo Cimento A (1971-1996), 1966
- Field Theory CommutatorsPhysical Review Letters, 1959
- Integral Representations of Causal CommutatorsPhysical Review B, 1958
- Potential in Quantum Field TheoryProgress of Theoretical Physics, 1955