1. Introduction

Of the many aspects of field theory explored by Umezawa during his lifelong research activity, none seems more central and more far reaching than the notion of ``boson condensation'' as a tool to induce structure in the ground state of a physical system. Boson condensation may lead to the formation of extended objects [1]. This idea permeates Umezawa's work in the last twenty five years and has inspired numerous original applications in such diverse fields as condensed matter physics, gauge models of particle physics and biology [2].
In retrospect, recognizing the influence of Umezawa's ideas on our own work, we have decided to investigate some new aspects of our current research on the theory of extended objects against the conceptual backdrop of the boson condensation approach. Even though our discussion is applicable to a generic p-brane embedded in a spacetime of arbitrary dimensions, the specific objects that we wish to consider presently are relativistic bubbles (2-branes in current terminology), because of their historic role in the development of QCD via the formulation of the so called ``bag models'' of hadrons and because of their increasingly important role in modern cosmology. In either case, one has to deal with a multiphase ground state characterized by the formation of domain walls separating regions of spacetime with different values of the vacuum energy density. Then, the question that we address in this paper is the search of a mechanism capable of inducing such a structure over the spacetime continuum. One possible answer, we contend, involves the process of boson condensation, and we are fairly confident that Umezawa would agree. We are not equally confident, however, that he would endorse our overall strategy without some qualifications. In fact, before plunging into a technical discussion of our work, it seems appropriate to recall the key conceptual steps of Umezawa's work for the sake of comparison with our own approach.
From Umezawa's vantage point, spatially extended objects, relativistic or not, arise as special solutions of local quantum field theories through the process of boson condensation. Some such solutions may have topological singularities, in the sense that the curl of the gradient of the boson condensation function is not necessarily zero. Once formed, extended objects may influence the original quantum system. This `` back reaction'' may be accounted for by a self-consistent potential attributed to the extended object.
The physical paradigm which reflects in full the above logical sequence is a type-II superconductor. In this system, an external magnetic field is squeezed into thin flux tubes by the vacuum pressure of the Cooper pairs condensate. It is this picture that we wish to extend to the case of relativistic bubbles minimally coupled to an antisymmetric tensor gauge potential $A _{\mu \nu \rho}(x)$. More specifically, the purpose of this paper is twofold: first, we wish to show how membrane condensation takes place inducing a two-phase structure in spacetime; second, we wish to show that membrane condensation can be driven by the quantum corrections of the gauge field $A _{\mu \nu \rho}(x)$, in analogy to the Coleman-Weinberg mechanism [3].
All of the above leads us to the interesting technical part of our discussion, to the analogy with superconductivity and to a comparison with Umezawa's approach.