Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-23
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, revtex4-1, 7 figures. v2: Small corrections in the fermion section and other typos
Scientific paper
We treat quantum back-reaction in time dependent processes for quantum field theory in various simplified models. The first example is a harmonic oscillator whose frequency depends on a second quantum variable $x$. Beginning with a classical analysis, we show how using a particular canonical transformation the system can be described by an improved adiabatic expansion with a velocity dependent force for $x$. We find an instability at a critical velocity that prevents integrating out the oscillator degree of freedom in the new variables. We extend this calculation to the quantum system and to field theory and describe how to study fermions with similar techniques. Finally, we set up a model with an abrupt change in the oscillator whose quantum mechanics can be solved exactly so that one can study the effects of back-reaction of a fully non-adiabatic change in a controlled setting. We comment on applications of these general results to the physics of D-branes, inflation, and black holes in AdS/CFT.
Asplund Curtis T.
Berenstein David
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