Search Results (3)

Within the finite-time-path out-of-equilibrium quantum field theory (QFT), we calculate direct photon emission from early stages of heavy ion collisions, from a narrow window, in which uncertainty relations are still important and they provide a new mechanism for production of photons. The basic difference with respect to earlier calculations, leading to diverging results, is that we use renormalized QED of quarks and photons. Our result is a finite contribution that is consistent with uncertainty relations. Full article

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological perturbation variable, and for the other, the canonically conjugate momentum, is defined, which is the strict requirement to define the time scale-separated quantum operators for OTOC and is perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism, not only one can study the quantum correlation during stochastic inflation and reheating, but can also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism, we study the phenomenon of quantum chaos by computing the expression for the Lyapunov spectrum. Furthermore, using the well known Maldacena Shenker Stanford (MSS) bound on the Lyapunov exponent, $\lambda \le 2\pi /\beta$, we propose a lower bound on the equilibrium temperature, $T=1/\beta$, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing, but not exponentially decaying, behaviour, which quantifies the random quantum correlation function out-of-equilibrium. We have also studied the classical limit of the OTOC and checked the consistency with the large time limiting behaviour of the correlation. Finally, we prove that the normalized version of OTOC is completely independent of the choice of the preferred definition of the cosmological perturbation variable. Full article

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in $g{\varphi }^3$ QFT, by using the retarded/advanced ( $R/A$ ) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We “repair” them, while keeping $d<4$ , to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy ${\Sigma }_F(p_0)$ does not vanish when $|p_0|\to \infty$ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object $G_F(p_0){\Sigma }_F(p_0)$ . In the FTP approach, after repairing the vertices, the corresponding composite objects are $G_R(p_0){\Sigma }_R(p_0)$ and ${\Sigma }_A(p_0)G_A(p_0)$ . In the limit $d\to 4$ , one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition $⟨0\left|\varphi \right|0⟩=0$ of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit $t\to \infty$ . Full article