On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

Abstract

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $\eta =1/2\ln [(t-z)/(t+z)]$ and the fluid proper time $\tau =(t^2-z^2{)}^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation.

References in corpus (6)

• Particle production in the central rapidity region
• Non-Perturbative Quark-Antiquark Production From a Constant Chromo-Electric Field via the Schwinger Mechanism
• Soft-Gluon Production Due to a Gluon Loop in a Constant Chromo-Electric Background Field
• Non-Perturbative Gluon pair production from a Constant Chromo-Electric Field via the Schwinger Mechanism in Arbitrary Gauge
• Separation of variables and exact solution of the Klein-Gordon and Dirac equations in an open universe
• Electrically neutral Dirac particles in the presence of external fields: exact solutions

Cited by in corpus (5)

• Theory and applications of free-electron vortex states
• Symmetries and Supersymmetries of the Dirac Hamiltonian with Axially-Deformed Scalar and Vector Potentials
• Fermion pair production in QED and the backreaction problem in (1+1)-dimensional boost-invariant coordinates revisited
• Backreaction and Particle Production in (3+1)-dimensional QED
• Pair creation in boost-invariantly expanding electric fields and two-particle correlations