We study the dynamics of a spherically symmetric relativistic
shell from the point of view of its Lagrangian and Hamiltonian
description. A spherically symmetric reduced Lagrangian is
obtained from an action principle: it gives an equation of
motion for the radial degree of freedom whose first integral
is Israel's junction condition. The relation between these
quantities, the generalized momentum and the Superhamiltonian
of the system is clarified.
Using the above defined dynamical setting vacuum decay is
pictured as the tunneling process between the bounded and
bounce trajectories of a shell separating two domains with
the de Sitter geometry (and different cosmologival constants).
The obtained result reproduces some results obtained with
different methods in the literature (in particular that of
S. Coleman and F. DeLuccia in Phys. Rev. D21 (1980)
3305 and that of S. Parke in Phys. Lett. 121B
(1983) 313) for the nucleation coefficient.
This agreement is a strong element in favor of the proposed
formalism. With it many results for the semiclassical dynamics
of relativistic shells can be obtained with routine calculations
involving functions of one variable and some parameters. This
gives the possibility of putting aside some technical problems
and of concentrating on the meaning and interpretation of
the results.
