Abstract
We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.
Highlights
A common question in many areas is the evaluation of correlations between several measurements, given the microscopic dynamics of the system
Using a quasi-classical approximation, we show that at tree level these correlations are dominated by fluctuations at the initial time
We have studied the correlation function between an arbitrary number of observables measured at equal times in quantum field theory
Summary
A common question in many areas is the evaluation of correlations between several measurements, given the microscopic dynamics of the system. 1-point functions (i.e. the expectation value of a local observable) are obtained from a classical solution of the field equation of motion, obeying a retarded boundary condition that depends on the initial state (φ = φ = 0 when the initial state is the perturbative vacuum) [11]. Their nextto-leading order (NLO) corrections are known [13], and can be expressed in terms of functional derivatives of this classical field with respect to its initial condition. In the appendix A, we derive some technical points used in the main part of the paper, while in the appendices B and C we discuss other types of initial states
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