Wick's Theorem for non-symmetric normal ordered products and contractions

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.Comment: 17 page

Gravitational wave signatures from kink proliferation on cosmic (super-) strings

Junctions on cosmic string loops give rise to the proliferation of sharp kinks. We study the effect of this proliferation on the gravitational wave (GW) signals emitted from string networks with junctions, assuming a scaling solution. We calculate the rate of occurrence and the distribution in amplitude of the GW bursts emitted at cusps and kinks in the frequency bands of LIGO and LISA as a function of the string tension, the number of sharp kinks on loops with junctions and the fraction of loops in the cosmological network which have junctions. Combining our results with current observational constraints, we find that pulsar data rule out a significant number of kinks on loops for strings with tensions G\mu > 10^{-12}. By contrast, for smaller tensions current observations allow for a large number of kinks on loops. If this is the case, the incoherent superposition of small bursts emitted at kink-kink encounters leads to an enhanced GW background that hides the strong individual bursts from kinks and cusps.Comment: 32 pages, 13 figure

On Normal ordering and Canonical transformations in Thermal Field Theory

We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer. We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.Comment: 13 pages, LaTeX. (Revisions made to discussion and various small errors in equations corrected

Gravitational Wave Bursts from Cosmic Superstrings with Y-junctions

Cosmic superstring loops generically contain strings of different tensions that meet at Y-junctions. These loops evolve non-periodically in time, and have cusps and kinks that interact with the junctions. We study the effect of junctions on the gravitational wave signal emanating from cosmic string cusps and kinks. We find that earlier results on the strength of individual bursts from cusps and kinks on strings without junctions remain largely unchanged, but junctions give rise to additional contributions to the gravitational wave signal coming from strings expanding at the speed of light at a junction and kinks passing through a junction.Comment: 20 pages, 5 figure

Racial variation in the number of spontaneous abortions before a first successful pregnancy, and effects on subsequent pregnancies.

OBJECTIVE: To assess the relationship between race and spontaneous abortion, whether the relationship varies by risk factors, and the effect of spontaneous abortions on subsequent pregnancies. METHODS: A retrospective study was undertaken using data collected in London, UK, between 1988 and 2000. Logistic regression evaluated histories of spontaneous abortion and associations with small-for-gestational-age and preterm births in black African, black Caribbean, and South Asian women relative to white European women. Interactions with risk factors were assessed. RESULTS: Overall, 196 040 women were included. Compared with white Europeans, the odds of a previous spontaneous abortion were increased in black African (adjusted odds ratio [aOR] 1.20; 95% confidence interval [CI] 1.12-1.29) and black Caribbean women (aOR 1.31; 95% CI 1.21-1.41). The strength of the association with black African race increased with age (P=0.002), and the association with South Asian race increased with age and body mass index (P<0.001 for both). Spontaneous abortion was associated with preterm birth in all races, but was strongest in black African women (aOR 1.47; 95% CI 1.29-1.67). CONCLUSION: The greater incidence of spontaneous abortion in black African and black Caribbean women should prompt further study of risk factors in relation to race. The interaction with age in black African and South Asian women could be important for counseling in relation to timing of pregnancy.This work was supported by a Medical Research Council PhD Studentship.This is the final published version. It first appeared at http://www.sciencedirect.com/science/article/pii/S002072921500123X