Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field

Understand

We derive a general exact form of the phase space distribution function and the thermal expectation values of local operators for the free quantum scalar field at equilibrium with rotation and acceleration in flat space-time without solving field equations in curvilinear coordinates.

• After factorizing the density operator with group theoretical methods, we obtain the exact form of the phase space distribution function as a formal series in thermal vorticity through an iterative method and we calculate thermal expectation values by means of analytic continuation techniques.
• We separately discuss the cases of pure rotation and pure acceleration and derive analytic results for the stress-energy tensor of the massless field.
• The expressions found agree with the exact analytic solutions obtained by solving the field equation in suitable curvilinear coordinates for the two cases at stake and already - or implicitly - known in literature.