ar X iv : g r - qc / 9 70 30 23 v 1 7 M ar 1 99 7 Can Temperature Be Quantized ?

It is shown that the temperature may be quantized in some spacetime due to the periodically topological structure of the Euclidean section. The quanta of the temperature is the Hawking-Unruh temperature. In the Euclidean quantum theory physical functions in the Lorentzian section of a complexified spacetime are assumed to be analytically continued from some functions in the Euclidean section [1, 2]. The non-trivial topological structure of the Euclidean section may cause some interesting effects in the Lorentzian section. For example, people have found that in a Lorentzian section whose corresponding Euclidean section is periodic in the Euclidean time τ = it there is the Hawking-Unruh effect (such as in the black hole spacetime and the de Sitter spacetime). In such a spacetime (Here we call it the Lorentzian Hawking-Unruh type spacetime (L-HU-spacetime), and call the corresponding Euclidean section the Euclidean Hawking-Unruh type spacetime (E-HU-spacetime)), observers whose worldlines are the integral curves of (∂/∂t) a , feel that they are in a thermal bath with the temperature T 0 = 1/β 0 = κ/2π, where β 0 is the period of the Euclidean time and κ is the surface gravity of the event horizon [3-5]. In this letter I show that in a L-HU-spacetime the temperature may be quantized with the quanta T 0 which is the lowest possible temperature for the thermal equilibrium.