Particle creation, classicality and related issues in quantum field theory: I. Formalism and toy models

Abstract

The quantum theory of a harmonic oscillator with a time dependent frequency arises i n s everal important physical problems, especially in the study of quantum field theory i n an external background. While the mathematics of t his system is straightforward, several conceptual issues arise i n such a study. We present a general formalism t o address some of t he conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. I n particular, we parameterize the wave function i n terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions—like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in–out states—are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Hav-ing developed the general formalism we apply it to several examples. Exact analytic expressions are found for a particular toy model and approximate analytic solutions are obtained in the extreme cases of adiabatic and highly non-adiabatic evolution. We then work out the exact results numerically for a variety of models and compare them with the analytic results and approximations. The formalism i suseful in addressing the question of emergence of classicality of the quantum state, its relation t o particle production and to clarify several conceptual issues relatedt ot his. In Paper II which is as equel to this, the formalism will be applied to analyze the corresponding issues in the context of quantum field theory i n background cosmological models and electric fields.