  We investigate the Unruh-Fulling effect in a class of nonlocal field theories
by examining both the number operator and Unruh-DeWitt detector methods. Unlike
in previous literature, we use Unruh quantization to quantize the matter field.
Such choice, as oppose to standard Minkowski decomposition, naturally
incorporates the time translational invariance in the positive frequency
Wightman function and thus captures the thermal equilibrium of the system. We
analyze the Unruh-Fulling effect for a massless real scalar field in both the
Lorentz noninvariant and Lorentz invariant nonlocal theories. In Lorentz
noninvariant nonlocal theory, the expectation value of number operator and the
response function of the detector are modified by an overall multiplicative
factor. Whereas in Lorentz invariant nonlocal theory these quantities remain
identical to those of the standard Unruh-Fulling effect. The temperature of the
thermal bath remains unaltered for both the Lorentz noninvariant and Lorentz
invariant nonlocal theories. Therefore, in terms of temperature, the nonlocal
Unruh-Fulling effect is universal while it is derived via Unruh quantization,
whereas the transition rate may be modified.
