Graham Shore

The U (1) Goldberger-Treiman relation and the two components of the proton “spin”

Abstract We present a simple and rigorous derivation of a recently proposed generalisation of the Goldberger-Treiman relation, and discuss its renormalisation group properties. We then show how to define separately isospin-conserving quark and gluon components of the proton “spin”, which evolve precisely as in the QCD parton model.

Quantum gravitational optics

In quantum theory, the curved spacetime of Einsteins general theory of relativity acts as a dispersive optical medium for the propagation of light. Gravitational rainbows and birefringence replace the classical picture of light rays mapping out the null geodesics of curved spacetime. Even more remarkably, superluminal propagation becomes a real possibility, raising the question of whether it is possible to send signals into the past. In this article, we review recent developments in the quantum theory of light propagation in general relativity and discuss whether superluminal light is compatible with causality.

'Faster than light' photons in gravitational fields: Causality, anomalies and horizons

Abstract A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a ‘horizon theorem’ which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation. These results are consequences of an effective action which in QED is valid only for low frequency photons. Their relevance to signal propagation and causality, which are controlled by high frequency propagation, is dependent on the dispersive properties of the modified propagation. This will be discussed elsewhere. A comparison is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.

The U(1) Goldberger-Treiman relation and the proton “spin”: A renormalisation group analysis

Abstract A detailed explanation of the U(1) Goldberger-Treiman relation is presented, and its renormalisation group properties discussed in detail. The implications for the proton “spin” problem are described, and a possible explanation for the small value of G A (0) inferred from the EMC experiment is given.

Superluminality and UV completion

Abstract The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity v ph ( 0 ) exceeds c . It is explained why causality is related not to v ph ( 0 ) but to the high-frequency limit v ph ( ∞ ) and how these are related by the Kramers–Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n ( ω ) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n ( ω ) is evaluated numerically and the role of the null energy condition T μ ν k μ k ν ⩾ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser–atom Λ -systems exhibiting Raman gain lines with Im n ( ω ) 0 . The possibility that a negative Im n ( ω ) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.

The refractive index of curved spacetime: The fate of causality in QED

Abstract It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime. Assuming the validity of the Kramers–Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of causality. Here, we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic. We find that the high-frequency limit of the phase velocity (i.e. the wavefront velocity) is always equal to c and causality is assured. However, the Kramers–Kronig dispersion relation is violated due to a non-analyticity of the refractive index in the upper-half complex plane, whose origin may be traced to the generic focusing property of null geodesic congruences and the existence of conjugate points. This makes the issue of micro-causality, i.e. the vanishing of commutators of field operators at spacelike separated points, a subtle one in local quantum field theory in curved spacetime.

“Faster than light” photons and charged black holes

Abstract Photons propagating in curved spacetime may, depending on their direction and polarisation, have velocities exceeding the “speed of light” c . This phenomenon arises through vacuum polarisation in QED and is a tidal gravitational effect depending on the local curvature. It implies that the Principle of Equivalence does not hold for interacting quantum field theories in curved spacetime. These results are illustrated for the propagation of photons in the Reissner-Nordstrom spacetime characterising a charged black hole. A general analysis of electromagnetic as well as gravitational birefringence is presented.

Strong equivalence, Lorentz and CPT violation, anti-hydrogen spectroscopy and gamma-ray burst polarimetry

Abstract The strong equivalence principle, local Lorentz invariance and CPT symmetry are fundamental ingredients of the quantum field theories used to describe elementary particle physics. Nevertheless, each may be violated by simple modifications to the dynamics while apparently preserving the essential fundamental structure of quantum field theory itself. In this paper, we analyse the construction of strong equivalence, Lorentz and CPT violating Lagrangians for QED and review and propose some experimental tests in the fields of astrophysical polarimetry and precision atomic spectroscopy. In particular, modifications of the Maxwell action predict a birefringent rotation of the direction of linearly polarised radiation from synchrotron emission which may be studied using radio galaxies or, potentially, gamma-ray bursts. In the Dirac sector, changes in atomic energy levels are predicted which may be probed in precision spectroscopy of hydrogen and anti-hydrogen atoms, notably in the Doppler-free, two-photon 1s–2s and 2s– n d ( n ∼ 10 ) transitions.

The causal structure of QED in curved spacetime: analyticity and the refractive index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.

Target independence of the EMC-SMC effect

Abstract An approach to deep inelastic scattering is described in which the matrix elements arising from the operator product expansion are factorised into composite operator propagators and proper vertex functions. In the case of polarised μp scattering, the composite operator propagator is identified with the square root of the QCD topological susceptibility √x′(0) , while the corresponding proper vertex is a renormalisation group invariant. We estimate x′(0) using QCD spectral sum rules and find that it is significantly suppressed relative to the OZI expectation. Assuming OZI is a good approximation for the proper vertex, our predictions, f01 d x g1p (x; Q2= 10 GeV2) = 0.143 ± 0.005 and GA0 = ΔΣ = 0.353 ± 0.052, are in excellent agreement with the new SMC data. This result, together with one confirming the validity of the OZI rule in the η′ radiative decay, supports our earlier conjecture that the suppression in the flavour singlet component of the first moment of gp observed by the EMC-SMC Collaboration is a target-independent feature of QCD related to the U(1) anomaly and is not a property of the proton structure. As a corollary, we extract the magnitude of higher twist effects from the neutron and Bjorken sum rules.