Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

All the arguments of a wavefunction are defined at the same instant, implying the notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts contradict the special relativity. We propose defining the wavefunction with respect to the invariant proper time of special relativity instead of the standard time. Moreover, we shall adopt the original idea of Schrodinger, suggesting that the wavefunction represents an ontological cloud-like object that we shall call “individual fabric” that has a finite density amplitude vanishing at infinity. Consequently, the action of measurement can be assimilated to the introduction of a confining potential that triggers an inherent nonlocal mechanism within the individual fabric. This mechanism is formalised by multiplying the wavefunction with a localising Gaussian, as in the GRW theory, but in a deterministic manner.

Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

All the arguments of a wavefunction are defined at the same instant implying a notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts are in contradiction with special relativity. We propose to define the wavefunction with respect to the invariant proper time of special relativity instead of standard time. Moreover, we shall adopt the original idea of Schrodinger suggesting that the wavefunction represents an ontological cloud-like object that we shall call ‘individual fabric’ that has a finite density amplitude vanishing at infinity. Consequently, measurement can be assimilated to a confining potential that triggers an inherent non-local mechanism within the individual fabric. It is formalised by multiplying the wavefunction with a localising gaussian as in the GRW theory but in a deterministic manner.

Aspects of quantum information in finite density field theory

We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

Holographic KMS relations at finite density

We extend the holographic Schwinger-Keldysh prescription introduced in [1] to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study the real time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in [2]. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dirac factors.