| Abstract: | We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator ({intlimits_{0} ^{infty}{rm e}^{iH_{0}t}zeta(frac{vert xvert }{R}) {rm e}^{-iH_{0}t}{rm d}t}), as ({R rightarrow infty}), is presented. Here, H0 is the free Dirac operator and ({zetaleft(tright)}) is such that ({zetaleft(tright) = 1}) for ({0 leq t leq 1}) and ({zetaleft(tright) = 0}) for ({t > 1}). This approach allows us to obtain the time delay operator ({delta mathcal{T}left(fright)}) for initial states f in ({mathcal{H} _{2}^{3/2+varepsilon}(mathbb{R}^{3};mathbb{C}^{4})}), ({varepsilon > 0}), the Sobolev space of order ({3/2+varepsilon}) and weight 2. The relation between the time delay operator ({deltamathcal{T}left(fright)}) and the Eisenbud–Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented. |
