Manifestations of Quantum Anomalies of Field Theory in Quantum Statistical Mechanics
- PDF / 330,354 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 79 Downloads / 155 Views
nifestations of Quantum Anomalies of Field Theory in Quantum Statistical Mechanics V. I. Zakharova, *, G. Yu. Prokhorovb, **, and O. V. Teryaevb, *** a
Alikhanov Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, Moscow, Russia b Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
Abstract—A new class of relations for statistically averaged matrix elements of different operators (such as Hamiltonian and conserved currents) is described in the one-loop approximation. The matrix elements have polynomial dependence on temperature and other thermodynamic values characterizing the equilibrium of the medium (the chemical potential, the angular velocity of rotation, and the acceleration). In this sense, the situation is analogous to the chiral anomaly in quantum field theory, which fixes the divergence of the axial current as a polynomial in external electromagnetic fields. Moreover, in this special case of matrix element of the axial current, it is possible to establish the relationship between the derivation of the anomaly and the oneloop expressions of statistical physics. The central role in establishing the correspondence is played by the polynomial Sommerfeld integrals. The generalizations of the one-loop relations in statistical physics are proposed, which (at least, today) have no analogs in quantum field theory. DOI: 10.1134/S1063779620040796
1. INTRODUCTION In the present work, we present a minisurvey of the recent results concerning computation of different matrix elements in a rotating and accelerating medium in the state of equilibrium. A more detailed discussion and further references may be found in [1–4]; although, we add some original comments. The study of statistical averages in a medium with acceleration and angular velocity of rotation is motivated, firstly, by the phenomenology of collisions of heavy ions based on the analysis of experimental data, see, e.g. [5]. The consideration is also interesting from the theoretical point of view. Indeed, although the state of equilibrium is usually characterized by the values of different chemical potentials conjugate to the conserved charges and by the angular velocity of rotation [6], in the relativistic case, this set of values is naturally supplemented by the acceleration, see [7–10] and the literature cited there. On the other hand, the acceleration may be introduced geometrically, via the metric of the Rindler space. The Rindler space has a boundary, or horizon. Thus, there appears a quite nontrivial relation between quantum statistical theory in Minkowski space and quantum field theory in a space with a boundary [1]. Our goal lies in studying the relativistic statistical effects, for which we use the technique of relativistic
quantum statistical mechanics. In contrast to the nonrelativistic theory, relativistic quantum statist
Data Loading...
