Thermal Aspects in Quantum Field Theory

Abstract

Thermal (or "KMS") states as well as ground states are characterized by analyticity properties in the (complexified) time variable. Such a characterization is applied to the quantum field theoretical systems on Minkowski, de Sitter and anti-de Sitter spacetimes. Privileged theories (or "vacua") can be defined on the basis of general principles which ensure "maximal" analyticity properties of the correlation functions. In such theories, there exists an observer-dependent thermal interpretation of the "vacuum" which is due to the (complex) geometry. In Minkowski spacetime, the (non-privileged) thermal quantum field theories at arbitrary temperature are investigated for their particle aspect at asymptotic times. This aspect is encoded in the corresponding two-point functions through a certain "damping factor", which is shown to depend on the dynamics of the interacting fields and suggests a possible substitute to the usual pole-particle concept in the thermal case.The first part of this talk (Sec 1-3) will be devoted to the following question: how does one determine the properties of stability of quantum states for relativistic systems which are described by local quantum fields, either in the Minkowskian background of flat spacetime, or more generally in certain curved spacetimes of simple type considered as given backgrounds for the quantum systems?. There is a general result of Pusz and Woronowicz [8] on quantum systems, according to which the class of quantum states satisfying an appropriate criterion of stability (called "passivity") can be partitioned into two subclasses, namely, on the one hand the "ground states" and on the other hand the "thermal equilibrium states" or "KMS states"; both cases are characterized by specific analyticity properties in the time-variable of the correlation functions of all pairs of local observables of the system. When one deals with a relativistic system in which the local observables are described in terms of quantum fields, it turns out that the "ground-state" or "thermal-state" interpretation of a stable state of the theory will in general depend on the motion of the local observer. While this phenomenon already occurs in flat spacetime with the Unruh effect [9], it seems to acquire a more general validity in curved spacetime by appearing as the manifestation of a certain type of "temporal curvature" of the world lines which is felt as a thermal effect by the corresponding observer. In models of spacetime equipped with a maximal symmetry group such as Minkowski, de Sitter and anti-de Sitter spacetimes, a specially * The results presented in the first part of this talk have been obtained in joint works with

É. Cartan’s Supersymmetric Universe and Our Detectors

“…Corresponding to changes of boundary conditions of temperature fields, path of fermions one can consider paths in complex temperature space. In addition to this temperature dependence there appears for quarks, Z 3 due to generalized Unruh effect [5].…”

“…We apply the topological structure of the 5 dimensional AdS spacetime which was studied by Bros et al [4,5] to the Cartan's octonion system. It predicts relations between the variable v = iβ used on the tuboid and the time t.…”

“…The two-point correlation functions at finite temperature which satisfy Kubo-Martin-Schwinger(KMS) was derived in C 5 [4,5]. The two point function of a state ω defines…”

“…In [2], it was claimed that crossing of 1/α i (Q) is a result of unphysical renormalization scheme, and when a supersymmetric evolution equation is solved, crossing of 1/α i (Q) never occurs but they can approach asymptotically. We consider complex orbits in 5 dimensional AdS space [4,5], and the model of supersymmetry is not same as [1][2][3]. We want to establish unification of the coupling constants at high energy leaving the problem of renormalization.…”

Non-perturbative insights into the spectral properties of QCD at finite temperature

“…• The structure of the discrete term implies that the dissipative effects experienced by particle states due to their interactions with the thermal medium is velocity dependent, as one would expect [20,24].…”