The complex time WKB approximation and particle production

The complex time WKB (CWKB) approximation has been an effective technique t o understand particle production in curved as well as in flat spacetime. Ea rlier we obtained the standard results on particle production in time-depen dent gauge in various curved spacetime, using the method of CWKB. In the pr esent work we generalize the technique of CWKB to the equivalent problems i n space-dependent gauge. Using CWKB, we first obtain the gauge invariant re sult for particle production in Minkowski spacetime in a strong electric fi eld. We then carry out particle production in de Sitter spacetime in space dependent gauge and obtain the same result that we obtained earlier in time dependent gauge. This ensures the gauge invariant description inherent in CWKB. The results obtained for de Sitter spacetime have an obvious extensio n to particle production in black hole spacetime. It is found that the orig in of the Planckian spectrum is due to repeated reflections between the tur ning points. As mentioned in earlier work, it is now explicitly shown that particle production is accompanied by rotation of currents.