Abstract
We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable non-equilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time \tau_0. As a consequence, the stress-energy tensor acquires non-trivial quantum corrections to the classical free-streaming form.
Highlights
Spurred by a successful description of experimental data in high-energy nuclear collisions, relativistic hydrodynamics has recently made major progress, both regarding its theoretical foundations as well as its phenomenological applications
We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable nonequilibrium problem
Even for the simplest case of a free scalar field, there are relevant quantum corrections related to its renormalization by subtraction of the vacuum expectation value
Summary
Spurred by a successful description of experimental data in high-energy nuclear collisions, relativistic hydrodynamics has recently made major progress, both regarding its theoretical foundations as well as its phenomenological applications. [13] offers a special opportunity to explore in detail some essential features of quantum relativistic hydrodynamics in a nonequilibrium situation and, in particular, to determine the pure quantum corrections to classical hydrodynamics and kinetic equations, including those to the stress-energy tensor and to the entropy current. In other words, this solution provides a benchmark test of a relativistic quantum fluid. IV we will present the field theory of the free neutral scalar field in the future light cone, including a diagonalization of the density operator This will put us in the position to calculate the thermal expectation value of the stress-energy.
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