Scenario for ultrarelativistic nuclear collisions. III. Gluons in the expanding geometry

Abstract

We derive expressions for various correlators of the gauge field and find the propagators in Hamiltonian dynamics which employs a new gauge A τ = 0. This gauge is a part of the wedge form of relativistic dynamics suggested earlier as a tool for the study of quantum dynamics in ultrarelativistic heavy ion collisions. We prove that the gauge is completely fixed. The gauge field is quantized and the field of radiation and the longitudinal fields are unambiguously separated. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid factorization.

Quark-antiquark production from classical fields in heavy-ion collisions:1+1dimensions

“…The flat metric is η ab = diag(1, −1) and the curved one g µν = diag(1, −τ 2 ), g µν = diag(1, −1/τ 2 ). The nonzero Christoffel symbols for the τ, η coordinates are [27] Γ τ ηη = τ and Γ η τ η = Γ η ητ = 1/τ . Given some representation for the usual γ-matrices in flat space, γ a , one can express the γ-matrices in curved coordinates as γ µ = e µ a γ a .…”

Classical Fields and Heavy Ion Collisions

“…The appearence of an adjoint scalar is analoguous to the way the time component of the gauge field becomes an adjoint scalar when dimensionally reducing high temperature gauge theory to a 3 dimensional effective theory [32]. Gauge field theory with an adjoint scalar field in the τ, η-coordinate system has been extensively studied in [171,172,173,174,175,176,177].…”

Quantum collisions of finite-size ultrarelativistic nuclei

“…This interaction resolves the nuclei constituents (e.g., the "partons", or "color dipoles") with the boost ν ≈ 0, and excite the quantum states with the boost ν ≈ 0. The wave functions of these states do not depend on the rapidity coordinate The propagators of the gauge fields in wedge dynamics were studied in [1,2]. In Appendix A, we review their properties with the emphasis on the needs of the present study.…”

“…The two viewpoints perfectly complement each other. The short scales of primary interaction provide a sufficient motivation to use the wedge dynamics which describes the fields inside the future domain of the "wedge" τ 2 = t 2 − z 2 > 0, and employs the "proper time" τ as a Hamiltonian time of the evolution and the coordinate rapidity η as a longitudinal coordinate [1,2]. The infamous rapidity plateau persistently observed in high-energy nuclear collisions strongly supports this picture.…”

“…Furthermore, the gauge A τ = 0 of the wedge dynamics can be fixed completely. Hence, the transverse and longitudinal fields are well separated and the gluon propagators of wedge dynamics have no spurious poles that can stimulate a singular 2 Addressing the issue of interaction of finite-size nuclei, one should keep in mind the source of the major difference between QED and QCD phenomena. The local gauge symmetry of QED can be extended to a global gauge symmetry which generates the conserved gauge-invariant global quantum number, the electric charge, which can be sensed at a distance.…”