This volume contains papers based on talks delivered at the Fourth Workshop on Quantum Field Theory Under the Influence of External Conditions. This series of workshops, held at the Institute for Theoretical Physics of the University of Leipzig, was launched in 1989. The present meeting took place 50 years after Hendrik B Casimir discovered the effect named after him. This effect was found by Casimir in investigating the retarded long range van der Waals forces in colloids and re-expressing them as a change in the vacuum energy of the electromagnetic field. The story of why this work was done was told by Casimir himself at the workshop. A historical account of the development of vacuum energy in quantum theory starting from Planck's half quanta was given by H Rechenberg. Another interesting topic was about a possible explanation of sonoluminescence as a dynamical Casimir effect. Kim Milton reported on the work done by Julian Schwinger on this topic during the last years of the great physicist's life, as well as on his own research. M Bordag (Leipzig) provided a general analysis of the ultraviolet divergences of the vacuum energy of a dielectric sphere.The Casimir effect had been experimentally verified 10 years after its discovery on a rather qualitative level. Only last year and in another experiment this year, it became also quantitatively well established. It turned out to be of unexpectedly high sensitivity with respect to the presence of the so-called fifth forces, as V Mostepanenko showed in his talk.Modern methods of computing the Casimir effect rely on zeta functional regularization and heat kernel expansion. This mathematical background, together with a broader embedding into expansions of various spectral quantities, was the subject of the talk by S Fulling. Recent progress in the computation of the heat kernel coefficients was reported by V Kornyak and K Kirsten.A number of talks were devoted to magnetic background fields of various types; for instance, new trends in the Aharonov–Bohm effect. In cosmology, negative energy densities and the role of adiabatic vacuum states in a de Sitter universe were discussed.
