General thermodynamic equilibrium with axial chemical potential for the free Dirac field

Abstract

We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential ${\mu }_A$. The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with ${\mu }_A\ne 0$. The appearance of these components might play an important role in chiral hydrodynamics.

29 pages, final version published in JHEP, typos

References in corpus (16)

• The Chiral Magnetic Effect
• Angular momentum conservation in heavy ion collisions at very high energy
• Relativistic Hydrodynamics with General Anomalous Charges
• Collisions in Chiral Kinetic Theory
• Nonlinear Responses of Chiral Fluids from Kinetic Theory
• Complete and Consistent Chiral Transport from Wigner Function Formalism
• Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid
• The eightfold way to dissipation
• Anomalous effects of dense matter under rotation
• A consistent description of kinetic equation with triangle anomaly
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Thermodynamical inequivalence of quantum stress-energy and spin tensors
• On axial current in rotating and accelerating medium
• Kubo formulas for thermodynamic transport coefficients
• Quantum non-equilibrium effects in rigidly-rotating thermal states
• Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames

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• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Unruh effect for fermions from the Zubarev density operator
• Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism
• Helical massive fermions under rotation
• Unruh effect universality: emergent conical geometry from density operator
• Extensivity, entropy current, area law and Unruh effect
• Thermodynamic equilibrium of massless fermions with vorticity, chirality and electromagnetic field
• Second-order Charge Currents and Stress Tensor in Chiral System
• Causal and stable first-order chiral hydrodynamics
• Spin polarization induced by magnetic field and the relativistic Barnett effect
• Anomalous gravitomagnetic moment and non-universality of the axial vortical effect at finite temperature
• Anomaly-induced transport phenomena from the imaginary-time formalism
• Calculation of acceleration effects using the Zubarev density operator
• Magneto-Transport in a Chiral Fluid from Kinetic Theory
• Quantum Kinetic Theory with Vector and Axial Gauge Fields
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Exact solutions in quantum field theory under rotation
• Chiral Vortical Effect in Extended Rarita-Schwinger Field Theory and Chiral Anomaly
• Shear-induced anomalous transport and charge asymmetry of triangular flow in heavy-ion collisions
• Gravitational chiral anomaly and anomalous transport for fields with spin 3/2
• Kubo formulas for spin polarization in dissipative relativistic spin hydrodynamics: a first-order gradient expansion approach
• Firewall boundaries and mixed phases of rotating quark matter in linear sigma model
• Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
• Fluid Acceleration in Heavy-Ion Collisions
• Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator