Decoherence in an Interacting Quantum Field Theory: The Vacuum Case

We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a "system field" and an "environment field" that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.Comment: 40 pages, published versio

The Scalar Field Kernel in Cosmological Spaces

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.Comment: 13 pages, 1 figur

Effect of the Trace Anomaly on the Cosmological Constant

It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this paper, however, we show by means of a semiclassical analysis that the trace anomaly does not affect the cosmological constant. We construct the effective action of the conformal anomaly for flat FLRW spacetimes consisting of local quadratic geometric curvature invariants. Counterterms are thus expected to influence the numerical value of the coefficients in the trace anomaly and we must therefore allow these parameters to vary. We calculate the evolution of the Hubble parameter in quasi de Sitter spacetime, where we restrict our Hubble parameter to vary slowly in time, and in FLRW spacetimes. We show dynamically that a Universe consisting of matter with a constant equation of state, a cosmological constant and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. When considering the trace anomaly truncated to quasi de Sitter spacetime, we find a region in parameter space where the quantum attractor destabilises. When considering the exact expression of the trace anomaly, a stability analysis shows that whenever the trace anomaly driven attractor is stable, the classical de Sitter attractor is unstable, and vice versa. Semiclassically, the trace anomaly does not affect the classical late time de Sitter attractor and hence it does not solve the cosmological constant problem.Comment: 18 pages, 11 figures, published versio

Decoherence in an Interacting Quantum Field Theory: Thermal Case

We study the decoherence of a renormalised quantum field theoretical system. We consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. Using out-of-equilibrium field theory techniques at finite temperatures, we show that the Gaussian von Neumann entropy for a pure quantum state asymptotes to the interacting thermal entropy. The decoherence rate can be well described by the single particle decay rate in our model. Connecting to electroweak baryogenesis scenarios, we moreover study the effects on the entropy of a changing mass of the system field. Finally, we compare our correlator approach to existing approaches to decoherence in the simple quantum mechanical analogue of our field theoretical model. The entropy following from the perturbative master equation suffers from physically unacceptable secular growth.Comment: 36 pages, 22 figure

Flavour-coherent propagators and Feynman rules: Covariant cQPA formulation

We present a simplified and generalized derivation of the flavour-coherent propagators and Feynman rules for the fermionic kinetic theory based on coherent quasiparticle approximation (cQPA). The new formulation immediately reveals the composite nature of the cQPA Wightman function as a product of two spectral functions and an effective two-point interaction vertex, which contains all quantum statistical and coherence information. We extend our previous work to the case of nonzero dispersive self-energy, which leads to a broader range of applications. By this scheme, we derive flavoured kinetic equations for local 2-point functions $S^{}_\mathbf{k}(t,t)$, which are reminiscent of the equations of motion for the density matrix. We emphasize that in our approach all the interaction terms are derived from first principles of nonequilibrium quantum field theory.Comment: 20 pages, 3 figures. Minor modifications, version published in JHE

Fermion Propagator in Cosmological Spaces with Constant Deceleration

We calculate the fermion propagator in FLRW spacetimes with constant deceleration $q=\epsilon-1$, $\epsilon=-\dot{H}/H^{2}$ for excited states. For fermions whose mass is generated by a scalar field through a Yukawa coupling $m=g_{\mathrm{\scriptscriptstyle{Y}}} \phi$, we assume $\phi \propto H$. We first solve for the mode functions by splitting the spinor into a direct product of helicity and chirality spinors. We also allow for non-vacuum states. We normalise the spinors using a consistent canonical quantisation and by requiring orthogonality of particle and anti-particle spinors. We apply our propagator to calculate the one loop effective action and renormalise using dimensional regularisation. Since the Hubble parameter is now treated dynamically, this paves the way to study the dynamical backreaction of fermions on the background spacetime.Comment: 18 pages, 1 figure, published versio

Entanglement entropy of black holes

The entanglement entropy is a fundamental quantity which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff which regulates the short-distance correlations. The geometrical nature of the entanglement entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in 4 and 6 dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields which non-minimally couple to gravity is emphasized. The holographic description of the entanglement entropy of the black hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in Relativit