From Green function to quantum field

A pedagogical introduction to the theory of a Gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function [Formula: see text] regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at [Formula: see text] starting from nothing but the retarded Green function [Formula: see text]. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished “vacuum” or “ground state”, and to recognize some interesting formal relationships, including a general condition on [Formula: see text] expressing zero-entropy or “purity”.

FURTHER ANALYSIS OF EXCITATIONS OF QUARKS AT FINITE TEMPERATURE — MASS EFFECT AND POLE STRUCTURE

We calculate the spectral function of the massive quark at finite temperature ( T ) using a Yukawa model and show that the peak in the negative energy region among the three-peaks found in a previous work for the massless quark is largely suppressed. To explore the underlying mechanism of this behavior, we also investigate the pole structure of the retarded Green function of the quark. We will show the result only for the massless quark. We find the residues of the poles corresponding the three-peaks are all comparable at T ∼ mb. We also show that the multi-peak structure of the quark spectra is well described in the pole approximation which indicates that the quasi-particle picture is valid in this T region.

EXPLICIT DERIVATION OF THE FLUCTUATION-DISSIPATION RELATION OF THE VACUUM NOISE IN THE N-DIMENSIONAL DE SITTER SPACE–TIME

Motivated by a recent work by Terashima (Phys. Rev.D60, 084001), we revisit the fluctuation-dissipation (FD) relation between the dissipative coefficient of a detector and the vacuum noise of fields in curved space–time. In an explicit manner we show that the dissipative coefficient obtained from classical equations of motion of the detector and the scalar (or Dirac) field satisfies the FD relation associated with the vacuum noise of the field, which demonstrates that Terashima's prescription works properly in the N-dimensional de Sitter space–time. This practice is useful not only to reconfirm the validity of the use of the retarded Green function to evaluate the dissipative coefficient from the classical equations of motion but also to understand why the derivation works properly, which is discussed in connection with previous investigations on the basis of the Kubo–Martin–Schwinger (KMS) condition. Possible application to black hole space–time is also briefly discussed.

A Generalized Effective Interaction

We discuss the possibility of neglecting poles of the effective interaction defined in a previous paper. In order to use model spaces which are not completely known we generalized the definition of the effective interaction considering as an example the self energy operator for the retarded Green-function.