Abstract
Using the Zubarev quantum-statistical density operator, we calculated the corrections to the energy-momentum tensor of a massless fermion gas associated with acceleration. It is shown that when fourth-order corrections are taken into account, the energy-momentum tensor in the laboratory frame is equal to zero at a proper temperature measured by a comoving observer equal to Unruh temperature. Consequently, the Minkowski vacuum is visible to the accelerated observer as a medium filled with a heat bath of particles with the Unruh temperature, which is the essence of the Unruh effect.
Highlights
INTRODUCTIONAccording to the standard formulation of the Unruh effect, an accelerated observer sees the Minkowski vacuum state as a thermal bath of particles with a temperature TU 1⁄4 2aπ, depending on the proper acceleration a [1,2,3,4]
According to the standard formulation of the Unruh effect, an accelerated observer sees the Minkowski vacuum state as a thermal bath of particles with a temperature TU 1⁄4 2aπ, depending on the proper acceleration a [1,2,3,4].The Unruh effect is most derived for scalar particles from consideration of the change in the ratio between positive and negative frequency modes of scalar fields in the proper time of the accelerated observer [1,4]
The Minkowski vacuum is visible to the accelerated observer as a medium filled with a heat bath of particles with the Unruh temperature, which is the essence of the Unruh effect
Summary
According to the standard formulation of the Unruh effect, an accelerated observer sees the Minkowski vacuum state as a thermal bath of particles with a temperature TU 1⁄4 2aπ, depending on the proper acceleration a [1,2,3,4]. [18], it was shown by calculating the values of quantum correlators for scalar fields at a finite temperature that the average value of any local operator turns out to be zero after subtracting of the vacuum contribution at the proper temperature, measured by a comoving observer, equal to the Unruh temperature. This fact means that the Minkowski vacuum is perceived by the accelerated observer as a medium filled with a thermal bath of particles with an Unruh temperature 2aπ, which is the essence of the Unruh effect. The proposed integral representation can be considered as a modification of this formula resulting from the Wigner function
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