THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.

/pdf/bibliographic-guide-to-the-foundations-of-quantum-mechanics-5bg1n4o4cz.pdf

Bibliographic guide to the foundations of quantum mechanics and quantum information

This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discussions. We pay special attention to the role of the equations of motion and to the relation between classical and quantum theories. Pointwise energy conditions were first introduced as physically reasonable restrictions on matter in the context of general relativity. They aim to express e.g. the positivity of mass or the attractiveness of gravity. Perhaps more importantly, they have been used as assumptions in mathematical relativity to prove singularity theorems and the non-existence of wormholes and similar exotic phenomena. However, the delicate balance between conceptual simplicity, general validity and strong results has faced serious challenges, because all pointwise energy conditions are systematically violated by quantum fields and also by some rather simple classical fields. In response to these challenges, weaker statements were introduced, such as quantum energy inequalities and averaged energy conditions. These have a larger range of validity and may still suffice to prove at least some of the earlier results. One of these conditions, the achronal averaged null energy condition, has recently received increased attention. It is expected to be a universal property of the dynamics of all gravitating physical matter, even in the context of semiclassical or quantum gravity.

Energy conditions in general relativity and quantum field theory

Quantum weak energy inequalities (QWEI) provide state-independent lower bounds on averages of the renormalized energy density of a quantum field. We derive QWEIs for the electromagnetic and massive spin-one fields in globally hyperbolic space–times whose Cauchy surfaces are compact and have trivial first homology group. These inequalities provide lower bounds on weighted averages of the renormalized energy density as “measured” along an arbitrary timelike trajectory, and are valid for arbitrary Hadamard states of the spin-one fields. The QWEI bound takes a particularly simple form for averaging along static trajectories in ultrastatic space–times; as specific examples we consider Minkowski space (in which case the topological restrictions may be dispensed with) and the static Einstein universe. A significant part of the paper is devoted to the definition and properties of Hadamard states of spin-one fields in curved space–times, particularly with regard to their microlocal behavior.

A quantum weak energy inequality for spin-one fields in curved space–time

Quantum weak energy inequalities (QWEI) provide state-independent lower bounds on averages of the renormalised energy density of a quantum field. We derive QWEIs for the electromagnetic and massive spin-one fields in globally hyperbolic spacetimes whose Cauchy surfaces are compact and have trivial first homology group. These inequalities provide lower bounds on weighted averages of the renormalized energy density as ``measured'' along an arbitrary timelike trajectory, and are valid for arbitrary Hadamard states of the spin-one fields. The QWEI bound takes a particularly simple form for averaging along static trajectories in ultrastatic spacetimes; as specific examples we consider Minkowski space [in which case the topological restrictions may be dispensed with] and the static Einstein universe. 
A significant part of the paper is devoted to the definition and properties of Hadamard states of spin-one fields in curved spacetimes, particularly with regard to their microlocal behaviour.

A Quantum Weak Energy Inequality for Spin-One Fields in Curved Spacetime

The quantum electrodynamics in presence of background external fields is developed. Modern methods of local quantum physics allow to formulate the theory on arbitrarily strong possibly time-dependent external fields. Non-linear observables which depend only locally on the external field are constructed. The tools necessary for this formulation, the parametrices of the Dirac operator, are investigated.

Quantum Electrodynamics on background external fields

We (re)consider the propagation of small disturbances (sound waves) in the presence of an irrotational vortex in a superfluid pinned/wound on a stiff central wire, with the help of the formalism of acoustic spacetimes. We give closed formulas for the scattering angle for sound rays, formulate the sound-propagation problem in the Hamiltonian form and discuss the form of boundary conditions at the core of the vortex, where the Hamiltonian has a singular point. The wave equation is simplified to a single ordinary differential equation of Mathieu type. We give an extensive discussion of perturbations localized close to the core, which are similar to what is known as the Kelvin waves for vortices that are bendable (not pinned). The spectra of modes depend strongly on the type of boundary condition employed close to the vortex core. The gapless mode with the angular number ?1, the Kelvin mode usually discussed in the context of unpinned vortices in superfluid helium or rotating Bose?Einstein condensates, turns out either not to exist or to have a completely different dispersion relation if the vortex is pinned. The question of whether or not the acoustic spacetime admits an ergoregion turns out to have a decisive (qualitative) influence on many aspects of sound-propagation phenomena.

Propagation of sound on line vortices in superfluids: role of ergoregions

We present a method based on the so-called Quantum Energy Inequalities, which allows to compare, and bound, the expectation values of energy-densities of ground states of quantum fields in spacetimes possessing isometric regions. The method supports the conclusion, that the Boulware energy density is universal both: at modest (and far) distances from compact spherical objects, and close to the would-be horizons of the gravastar/QBHO spacetimes. It also provides a natural consistency check for concrete (approximate, numerical) calculations of the expectation values of the energy-momentum tensors.

On Quantum Effects in the Vicinity of Would-Be Horizons

We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.

Spontaneous emission of light from atoms: the model

In this paper a rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter’s interior cosmological solution when the angular momentum goes to zero. This solution is locally isomorphic to de Sitter space, but as one approaches the axis of rotation it has a novel feature: a conical event horizon. This suggests that in reality rotating compact objects have a vortex structure similar to that conjectured for rotating superfluid droplets. In the limit of slow rotation the vortex core would be nearly cylindrical and the space-time inside � �

A vortex model for rotating compact objects

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