We calculate the fermion propagator in Friedmann-Lemaître-RobertsonWalker (FLRW) spacetimes with constant deceleration q = −1, = −Ḣ /H 2 for excited states. For fermions whose mass is generated by a scalar field through a Yukawa coupling m = g Y φ, we assume φ ∝ H . We first solve the mode functions by splitting the spinor into a direct product of helicity and chirality spinors. We also allow for non-vacuum states. We normalize the spinors using a consistent canonical quantization and by requiring orthogonality of particle and anti-particle spinors. We apply our propagator to calculate the one-loop effective action and renormalize using dimensional regularization. Since the Hubble parameter is now treated dynamically, this paves the way to study the dynamical backreaction of fermions on the background spacetime.

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states. PACS numbers: 03.65.Yz, 03.70.+k, 03.67.-a, 98.80.-k I. INTRODUCTIONThe most natural way of defining the entropy of a quantum system is to use the von Neumann entropy:whereρ denotes the density operator which in the Schrödinger picture satisfies the von Neumann equation:whereĤ is the Hamiltonian. Since quantum mechanics and quantum field theory are unitary theories, the von Neumann entropy is conserved, albeit in general not zero. The decoherence program [1, 2] usually assumes the existence of some environment that is barely observable to some observer. This allows us to construct a reduced density operatorρ red characterising the system S, which is obtained by tracing over the unobservable environmental degrees of freedom E:ρ red = Tr E [ρ]. This is a non-unitary process which consequently generates entropy. This operation is justified by the observer's inability to see the environmental degrees of freedom (or better: access the information stored in the ES-correlators). Yet, tracing out some degrees of freedom results in complications. The simple looking von Neumann equation (2) is replaced by an equation for the reduced density operator. This "master equation" [3,4] can be solved for only in very simple situations, which has hampered progress in decoherence studies in the context of interacting quantum field theories. In particular, we are not aware of any known solution of the master equation that would include perturbative corrections and implement the program of renormalisation. Also, one has no control of the error in a calculation in the perturbative sense induced by neglecting non-Gaussian corrections.Here we propose a decoherence program that can be implemented in a field theoretical setting and that also allows us to incorporate renormalisation procedures. The idea is very simple, and we present it for a real scalar field φ(x). A generalisation to other types of fields, e.g. gauge and fermionic fields, should be quite straightforward.The density matrixρ(t) contains all information about the (possibly mixed) state a quantum system is in. From the density matrix one can, in principle, calculate various correlators. For example, the three Gaussian correlators * J.F.Koksma@uu.nl, T.Prokopec@uu.nl, M.G.Schmidt@thphys.uni-heidelberg.de 1 As a simple example, consider the temperature correlations induced by scalar field perturbations from inflation: while the amplitude ...

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 selfenergy 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.

One hope to solve the cosmological constant problem is to identify a symmetry principle, based on which the cosmological constant can be reduced either to zero, or to a tiny value. Here, we note that requiring that the vacuum state is Lorentz invariant significantly reduces the theoretical value of the vacuum energy density. Hence, this also reduces the discrepancy between the observed value of the cosmological constant and its theoretical expectation, down from 123 orders of magnitude to 56 orders of magnitude. We find that, at one loop level, massless particles do not yield any contribution to the cosmological constant. Another important consequence of Lorentz symmetry is stabilization of the gravitational hierarchy: the cosmological constant (divided by Newton's constant) does not run as the quartic power of the renormalization group scale, but instead only logarithmically.