We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Because of the long-range interaction between junctions in layered superconductors, the calculated MQT escape rate Gamma has a nonlinear dependence on the number of junctions in the stack. We show that the crossover temperature between quantum and thermal escape increases when increasing the number of junctions. This allows us to quantitatively describe striking recent experiments in Bi2Sr2CaCu2O8+delta stacks.