Symmetry breaking in inhomogeneous spacetimes: A tractable example

Symmetry breaking in Rindler space viewed as a prototypical example of an inhomogeneous spacetime is discussed. It is shown that classically for a massless self-interacting scalar field there are at least two possible field configurations which are minima of the classical action. Only one of these is a minimum of the Rindler Hamiltonian, however, the nonglobal minimum being a state of broken symmetry and existing solely as a consequence of the inhomogeneity of the spacetime. It is noted that this state could not be found by any type of quasilocal analysis. At the one-loop level the field acquires a ‘‘dynamical’’ mass which is spatially dependent and tachyonic thus rendering the classical ground state quantum-mechanically unstable. A self-consistent solution to the background-field equations is found which turns out to be the classical broken-symmetry state in the limit of weak coupling. This state is stable at the one-loop level. Some pertinent remarks about the notion of mass for accelerated observers is given.