Abstract
We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called “Kubo formulae”. We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.
Highlights
We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics
This result is precisely the same found in recent calculations of the mean axial current related to the chiral vortical effect (CVE), which is the onset of a vector current along the vorticity due to the axial anomaly
We have studied quantum relativistic free fields of spin 0 and 1/2 at general thermodynamic equilibrium with non-vanishing acceleration and vorticity and we have calculated the thermodynamic coefficients of a second-order expansion of the stress-energy tensor in thermal vorticity tensor, which includes acceleration and vorticity vectors, with a finite value of the chemical potential
Summary
The general covariant form of the local thermodynamic equilibrium density operator was introduced in [36,37,38] and lately discussed in detail in refs. [23, 30, 39,40,41]: ρ. If = 0 there are spacetime regions where β is spacelike or lightlike, like in the rotating case (2.8) This does not undermine the possibility to calculate the mean value of local operators in the regions where β is timelike. Thereby, the zero-order term is the same mean value as at homogeneous global equilibrium with four-temperature equal to the β field in x and corrections arise form a power series in. This method was presented and applied in ref. This method was presented and applied in ref. [30] for local operators of the free scalar field and it will be outlined
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