Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-08-09
Gen.Rel.Grav. 40 (2008) 661-708
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTeX 4; 32 pages; 28 figures; first of a series of two papers, the second being arXiv:0708.1237 [gr-qc]; high resolution fig
Scientific paper
10.1007/s10714-007-0526-z
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parametrize the wave function in 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. Having 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 is useful in addressing the question of emergence of classicality of the quantum state, its relation to particle production and to clarify several conceptual issues related to this. In Paper II (arXiv:0708.1237), which is a sequel to this, the formalism will be applied to analyze the corresponding issues in the context of quantum field theory in background cosmological models and electric fields.
Mahajan Gaurang
Padmanabhan Thanu
No associations
LandOfFree
Particle creation, classicality and related issues in quantum field theory: I. Formalism and toy models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Particle creation, classicality and related issues in quantum field theory: I. Formalism and toy models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Particle creation, classicality and related issues in quantum field theory: I. Formalism and toy models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-417188