Different Interpretations of the Particle Production in Quantum Fields Theory

We discuss different interpretations of the particle production in quantum fields theory. We study in detail the “instantaneous Hamiltonian diagonalization method” and the “adiabatic vacuum prescription” and we show the difference between both methods calculating the particle production in the flat Friedmann-Robertson-Walker chart of the de Sitter space-time. Finally, we study the particle production in a classically forbidden region, and we apply the obtained results to the problem of the catastrophic particle production in tunneling universes.