International Journal of Modern Physics A

The linear scalar quantum field, propagating in a globally hyperbolic space–time, is a relatively simple physical model that allows us to study many aspects in explicit detail. In this review, we focus on the thermal equilibrium (KMS) states of such a field in a stationary space–time. Our presentation draws on several existing sources and aims to give a unified exposition, while weakening certain technical assumptions. In particular we drop all assumptions on the behavior of the time-like Killing field, which is important for physical applications to the exterior region of a stationary black hole.

Our review includes results on the existence and uniqueness of ground and KMS states, as well as an evaluation of the evidence supporting the KMS-condition as a characterization of thermal equilibrium. We draw attention to the poorly understood behavior of the temperature of the quantum field with respect to locality.

If the space–time is standard static, the analysis can be done more explicitly. For compact Cauchy surfaces we consider Gibbs states and their properties. For general Cauchy surfaces we give a detailed justification of the Wick rotation, including the explicit determination of the Killing time dependence of the quasi-free KMS states.

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained.

A rank-three tensor model in canonical formalism has recently been proposed. The model describes consistent local-time evolutions of fuzzy spaces through a set of first-class constraints which form an on-shell closed algebra with structure functions. In fact, the algebra provides an algebraically consistent discretization of the Dirac–DeWitt constraint algebra in the canonical formalism of general relativity. However, the configuration space of this model contains obvious degeneracies of representing identical fuzzy spaces. In this paper, to delete the degeneracies, another first-class constraint representing a scaling symmetry is added to propose a new canonical rank-three tensor model. A consequence is that, while classical solutions of the previous model have typically runaway or vanishing behaviors, the new model has a compact configuration space and its classical solutions asymptotically approach either fixed points or cyclic orbits in time evolution. Among others, fixed points contain configurations with group symmetries, and may represent stationary symmetric fuzzy spaces. Another consequence on the uniqueness of the local Hamiltonian constraint is also discussed, and a minimal canonical tensor model, which is unique, is given.

A general expression for the dead cone of gluons radiated by virtual partons has been derived. The conventional dead cone for massive on-shell quarks and the dead cone for the virtual partons have been obtained by using different limits of the general expression. Radiative suppression due to the virtuality of initial parton jets in heavy-ion collisions has been discussed. It is observed that the suppression caused by the high virtuality is overwhelmingly large as compared to that on account of conventional dead cone of heavy quarks.

The fragmentation function at high energy experiments is introduced by using thermofield dynamics (TFD), a real-time finite-temperature quantum field formalism. Due to the structure of TFD, the results at T = 0 and T ≠ 0 are split in a direct way. As an application, we consider the temperature effect on the fragmentation function of a hadron leading to quark–antiquark pairs. Using a definition of Wilson-loop in real-time, we find that the fragmentation function decreases in magnitude with an increase in the temperature.

We study the 3-form gauge theory in the context of generalized BRST formulation. We construct the finite field-dependent BRST symmetry for such a theory. The generating functional for 3-form gauge theory in noncovariant gauge is obtained from that of covariant gauge. We further extend the results by considering 3-form gauge theory in the context of Batalin–Vilkovisky formulation.

We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called i-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang–Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined Källén–Lehmann spectral representation, thus allowing for a particle interpretation. These physical excitations would correspond to the "mesons" of the model, the latter being bound states of two unphysical i-particles. The meson mass is explicitly estimated from the pole emerging in a resummed class of diagrams. The main purpose of this paper is thus to explicitly verify how a real mass pole can and does emerge out of constituent i-particles that have complex masses.