How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein's gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity. A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell's equations expressed in terms of the excitation H=(D,H) and the field strength F=(E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H= functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al. (eds.). Springer, Berlin (2000) to be published (Revised version uses Springer Latex macros; Sec. 6 substantially rewritten; appendices removed; the list of references updated

Some aspects of the Liouville equation in mathematical physics and statistical mechanics

This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE)

Cytotoxicity of KDEL-terminated ricin toxins correlates with distribution of the KDEL receptor in the Golgi

Journal of Histochemistry and Cytochemistry442159-165JHCY

Mature maternity: Long term associations in first children born to older mothers in 1970 in the UK

Study objectives - To identify the physical, behavioural, medical, and educational outcomes in first children born to women aged 30 or more compared with those born to younger women. Design - Longitudinal cohort study design employing logistic regression analysis of data obtained from the British births survey of 1970 and the child health and education study follow ups to this cohort at ages 5 and 10. Setting - One week birth cohort covering the whole of the United Kingdom. Participants - The carers of 4315 first children born to women during the week of April 5th-llth 1970 inclusive in the whole of the United Kingdom except Northern Ireland, and followed up at both 5 and 10 years of age. In addition, information was obtained from health visitors, the child's teacher at 10, and the medical officer who completed an examination. At 10 the child also completed a questionnaire. Measurements - Data were obtained from questionnaires administered to the carers of the child at each time point, from their teacher at age 10, and from the results of a medical examination at age 10. Educational tests were also conducted at this age. Main results - Having adjusted for the effects of confounding factors, late primiparity was significantly associated with a number of events in labour and delivery involving obstetric interventions ranging from induction to operative deliveries and general anaesthesia. At 5 years of age, controlling additionally for family size at that time, associations were found between late primiparity and fewer adverse measures of behaviour in the child. Both the child's head circumference and the score on a picture based vocabulary test at this age were slightly greater in the index group. At 10 years of age, adjusting for background factors and present family size, late primiparity was associated with few outcome measures. Children born to older mothers, however, scored slightly higher on a broad range of educational tests administered at school. Conclusions - No clearly demonstrable adverse outcomes could be linked to later primiparity in the 1970 child health and education study national cohort study. Modest behavioural and educational advantages were detected in the group witholder first-time mothers. A woman's later primiparity may be associated with their child having a slightly larger head circumference compared with whole of the rest of the study cohort