Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar $φ^4$

Abstract

We study the evolution of the non-equilibrium quantum fields from a highly excited initial state in two approaches: the standard Keldysh-Schwinger diagram technique and the semiclassical expansion. We demonstrate explicitly that these two approaches coincide if the coupling constant g and the Plank constant are small simultaneously. Also, we discuss loop diagrams of the perturbative approach, which are summed up by the leading order term of the semiclassical expansion. As an example, we consider shear viscosity for the scalar field theory at the leading semiclassical order. We introduce the new technique that unifies both semiclassical and diagrammatic approaches and open the possibility to perform the resummation of the semiclassical contributions.

Curved space equilibration vs. flat space thermalization (a short review)

“…As in the situation described in the section 4, the secular memory contribution may come from the sunset two-loop diagram correction to the Keldysh propagator. In the limit (18) the corrected propagator has the same form as ( 16), but with the following expressions in place of n 0 p and κ 0 p [20]:…”

“…In fact, we could have chosen an initial state of the form (13) with n 0 p = 0 and κ 0 p = 0 rather than Fock space ground state, a p |α, β = 0, meanwhile keeping the same basis of modes (25). Then, the form of the loop corrections in the limit (18) would have been different both from (24) and from ( 19), ( 20) [22].…”

“…In such a case one has a + p a q = n p, q and a p a q = κ p, q . (See e.g [18]. on how to deal with generic initial states.)…”

Classical and quantum butterfly effect in nonlinear vector mechanics

“…However, we prefer to work with the original model ( 1.3) because it offers a clear setup for the calculation of real-time propagators. First, it allows us to define the initial quantum state with respect to the free (Gaussian) Hamiltonian and then to turn on the coupling constant adiabatically, which is necessary to ensure the validity of Wick's theorem [86][87][88][89]. In the theory after the Hubbard-Stratonovich transformation, this approach can potentially lead to a 0/0 indeterminacy, so it should be used carefully.…”

Particle creation in nonstationary large N quantum mechanics

“…Schwinger-Keldysh technique is a powerful tool to calculate correlation functions and quantum averages in nonstationary situations [39][40][41][42][43][44]. This technique can be concisely described by the following path integral [64][65][66]:…”