QUANTUM INEQUALITIES IN 2-DIMENSIONAL MINKOWSKI SPACETIME

We generalize some results of Ford and Roman constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two-dimensional Minkowski spacetime. Ford an d Roman showed that the energy density measured by an inertial observe r, when averaged with respect to the observers proper time by integrat ing against some weighting function, is bounded below by a negative lo wer bound proportional to the reciprocal of the square of the averagin g time scale. However, the proof required a particular choice for the weighting function. We extend the Ford-Roman result in two ways. (i) W e calculate the optimum (maximum possible) lower bound and characteriz e the state which achieves this lower bound; the optimum lower bound d iffers by a factor of six from the bound derived by Ford and Roman for their choice of smearing function. (ii) We calculate the lower bound for arbitrary, smooth positive weighting functions. We also derive sim ilar lower bounds on the spatial average of energy density at a fixed moment of time. [S0556-2821(97)07420-1]. PACS number(s): 04.62.+v, 03. 70.+k, 42.50.Dv.