Advanced Green Functions Research Articles

On the existence of weakly retarded and advanced Green's functions

By considering a model field equation that contains the acausal propagation features of a spin 3/2 field we show that depending on the ``external field'' one can either have weakly retarded fundamental solutions or not.

On the Green's Functions for the Bethe-Salpeter Equation

We have studied four possible Green's functions of the Bethe-Salpeter equation for equal mass scalar bosons by considering contours in an off-the-mass-shell complex energy (Ω) plane and an on-the-mass-shell magnitude of 3-momenta (k) or energy (ωk) complex plane. We find that three of the Green's functions—causal, retarded, and advanced Green's function—cannot lead to scattering solutions. Only a new Green's function, which we have called the scattering Green's function, with appropriate restrictions on the interaction V(x), can lead to scattering states.

Correlation functions and Green functions: zero-frequency anomalies

The zero-frequency anomaly that can arise in the Fourier transform of certain quantum mechanical correlation functions is investigated. Two physical interpretations are given to the anomalous term. It is shown that any method for calculating the thermal Green function (though not the retarded or advanced commutator Green functions) should also yield the strength of the anomaly. An example is given. A critical discussion is given of recent contributions by other authors.

Spectral representations of the mass and polarisation operators at arbitrary temperatures

The spectral representation of the mass operator at zero temperature is generalized to the case of an arbitrary temperature. For convenience, retarded and advanced Green functions are used because they possess simple analytic properties at any temperature. In a iike manner, photon or phonon retarded or advanced Green functions are used to define the polarization operator. (H.D.R.)