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In quantum field theory, there exist states in which the expectation value of the energy density for a quantized field is negative. These negative energy densities lead to many problems. Although quantum field theory introduces negative…
In classical physics the energy density of a field, such as the electromagnetic field, is always positive. However, in quantum field theory it has been shown that the energy density can be negative. There are restrictions, called the…
It is generally known that the energy density can be negative in quantum field theory. It is also believed that there are limits on this negative energy density. These limits are known as the quantum inequalities. In a recent paper [8] an…
Quantum fields are well known to violate the weak energy condition of general relativity: the renormalised energy density at any given point is unbounded from below as a function of the quantum state. By contrast, for the scalar and…
We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum…
The quantum interest conjecture of Ford and Roman states that any negative energy flux in a free quantum field must be preceded or followed by a positive flux of greater magnitude, and the surplus of positive energy grows the further the…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to…
Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background…
Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These…
Energy densities of the quantum states that are superposition of two multi-electron-positron states are examined. It is shown that the energy densities can be negative only when two multi-particle states have the same number of electrons…
We study a phenomenon occuring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise nonnegative may assume arbitrarily negative expectation values after quantisation,…
Certain exotic phenomena in general relativity, such as backward time travel, appear to require the presence of matter with negative energy. While quantum fields are a possible source of negative energy densities, there are lower bounds -…
Quantum Weak Energy Inequalities (QWEIs) are results which limit the extent to which the smeared renormalised energy density of a quantum field can be negative. On globally hyperbolic spacetimes the massive quantum Dirac field is known to…
It is well known that the energy density of a quantum state can be negative. It has been shown that there are limits on this negative energy density which are called the quantum inequalities. In this paper we will demonstrate an example of…
Quantum inequalities (QI's) provide lower bounds on the averaged energy density of a quantum field. We show how the QI's for massless scalar fields in even dimensional Minkowski space may be reformulated in terms of the positivity of a…
Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the…
Fewster and Mistry have given an explicit, non-optimal quantum weak energy inequality that constrains the smeared energy density of Dirac fields in Minkowski spacetime. Here, their argument is adapted to the case of flat, two-dimensional…
The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The…
Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the…