Temperature of the Vacuum Accelerated by External Fields

Using the result of M\"uller et al. [1], we show that in a constant electric field $E$, the electron fluctuations $\langle \bar\psi\psi\rangle$ display a thermal Bose spectrum with temperature $T=eE/m\pi=a/\pi$. This result contrasts with the Fermi spectrum and Hawking-Unruh temperature $T_{HU}=a/2\pi$ expected from viewing the vacuum fluctuations of the electrons as accelerated [2,3]. We consider the temperature in the electric field as a function of magnetic moment $g$. We find that the temperature in the electric field arises from the Dirac spinor nature of the electron with $g=2$ and, setting arbitrarily $g=1$, we recover the Hawking-Unruh $T_{HU}=a/2\pi$ with a Fermi spectrum. \\[4pt] [1] B. Muller, W. Greiner, and J. Rafelski, Phys. Lett. A63, 181 (1977).\\[0pt] [2] L.C.B. Crispino, A. Higuchi, George E.A. Matsas, Rev. Mod. Phys. 80, 787 (2008).\\[0pt] [3] W.-Y. Pauchy Hwang and S. P. Kim, Phys.Rev. D80, 065004 (2009).