Biological rhythms are detected in a variety of physiological and pathological conditions in man and animals, such as rheumatoid arthritis and asthma. Here we describe a circadian rhythm in experimental infectious and non-infectious granuloma. After 30 days of BCG (Bacillus Calmette-Guerin) or nystatin inoculation in the left hind foot of C57B1/6 mice, there is an oscillation with a period of approximately 24 hr in the variation of paw thickness, indicating a circadian rhythm. The acrophase occurred during the light phase, between 9:00 and 13:00 hr, while the nadir occurred in the dark phase, between 21:00 and 01:00 hr. The vascular permeability around the granulomatous lesions was higher at 12:00 hr than at 24:00 hr. This is in agreement with the observation that the thickness of a paw with granulomatous lesion is larger during the light phase. This rhythmic variation was eliminated by either pinealectomy or superior cervical ganglionectomy, which greatly reduce melatonin levels in the blood. Nocturnal replacement of melatonin in pinealectomized mice led to the re-establishment of the circadian rhythm. Thus, the rhythm of the granulomatous lesion is due to the rhythmic melatonin release by the pineal gland. This approach opens new questions regarding the modulation of chronic inflammation in inflammatory diseases that present rhythmic symptoms throughout the day.

A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The orthogonality and completeness relations of the Fourier basis are derived in the same way. It is shown that the limiting function of any Fourier series is also the limit to the unit circle of an analytic function in the open unit disk. An alternative way to recover the original real functions from the Fourier coefficients, which works even when the Fourier series are divergent, is thus presented. The convergence issues are discussed up to a certain point. Other possible uses of the correspondence established are pointed out.

Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of QED 3 . The theory is thus rephrased in terms of a massive vector boson whose mass is e 2 /(8π). Subsequently, it is shown that electron-electron bound states are possible in QED 3 .

We carry out the Hamiltonian quantization of a member of a class of' gauge theories in which the internal metric becomes an independent degree of freedom and the gauge group is generalized to SL( N , C ) . The Hamiltonian quantization is carried out both in a gauge where only the SU(,V) synimetry is manifest and in a gauge-invariant way. These theories have been proposed by Cahill, and they also arise as the nongravitational sector of a unified theory of gravitational and gauge fields which has been proposed by one of us (J.D.). The physical degrees of freedom are identified and a relativistically invariant functional generator is constructed. The resulting quantum theory is stable, but not perturbatively renormalizable.

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