This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researchers in theoretical physics, especially those with an interest in experimental and theoretical particle physics and quantum field theory.

Phase transitions create a domain structure with defects, that has been argued by Zurek and Kibble to depend in a characteristic way on the quench rate. In this letter we present an experiment to measure the ZK scaling exponent σ. Using long symmetric Josephson Tunnel Junctions, for which the predicted index is σ = 0.25, we find σ = 0.27 ± 0.05. Further, we agree with the ZK prediction for the overall normalisation.

We report on the first experimental verification of the Zurek-Kibble scenario in an isolated superconducting ring over a wide parameter range. The probability of creating a single flux quantum spontaneously during the fast normal-superconducting phase transition of a wide Nb loop clearly follows an allometric dependence on the quenching time τ Q , as one would expect if the transition took place as fast as causality permits. However, the observed Zurek-Kibble scaling exponent σ = 0.62 ± 0.15 is two times larger than anticipated for large loops. Assuming Gaussian winding number densities we show that this doubling is well-founded for small annuli.

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It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss an improved experiment for measuring the scaling exponent for the production of single fluxons in annular symmetric Josephson tunnel junctions. We find Ӎ 0.5 and show how this can arise from the Kibble-Zurek scenario. Further, we report accurate measurements of the temperature dependence of the junction gap voltage, which allow for precise monitoring of the fast temperature variations during the quench.