Klein-Gordon equation from Maxwell-Lorentz dynamics

We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the Lagrangian submanifolds of the phase space when it is endowed with the symplectic structure modified by the electromagnetic field. We have found that the existence of this type of solution leads us directly to the Klein-Gordon equation as a compatibility condition. Therefore, surprisingly, quite natural assumptions on the classical theory involve a quantum condition without any process of limit. This result could be a partial response to the inquiries of Dirac.Comment: 8 pages; some misprints corrected; added some coments in the abstract and also explaining the relationship with the work of P.A.M. Dirac; also added 2 reference

A Review of the Dermatological Complications of Giant Cell Arteritis

Giant cell arteritis (GCA) is characterized by granulomatous inflammation of large and medium-sized vessels. It is the most common vasculitis among elderly people in Europe and North America. GCA usually presents with ischemic cranial manifestations such as headache, scalp tenderness, visual manifestations, and claudication of the tongue and jaw. Thickness and tenderness of temporal arteries are the most recognizable signs of GCA on physical examination. Laboratory tests usually show raised acute phase reactants. Skin manifestations are uncommon in GCA and are rarely found as a presenting symptom of GCA. Necrosis of the scalp and tongue is the most common ischemic cutaneous manifestation of GCA. Although infrequent, when present it reflects severe affection and poor prognosis of GCA. Panniculitis-like lesions have been reported in the setting of GCA, with nodules being the most common finding. Other entities, such as generalized granuloma annulare or basal cell carcinoma have been occasionally described in GCA patients. Prompt recognition and initiation of therapy are crucial to prevent serious complications of GCA. When high suspicion of GCA exists, immediate administration of glucocorticoids is recommended. It is advisable to refer the patient to a specialist GCA team for further multidisciplinary assessment.Funding: This line of research on vasculitis was partially supported by RETICS Programs, RD08/0075 (RIER), RD12/0009/ 0013 and RD16/0012 from “Instituto de Salud Carlos III” (ISCIII) (Spain)

Bone Metabolism in Patients with Hidradenitis Suppurativa: A Case-control Study

Hidradenitis suppurativa (HS) is a chronic inflammatory disease of the hair follicles. The aim of this case-control study was to assess whether HS is associated with disturbances in trabecular bone score, bone mineral density, bone remodelling markers, and calciotropic hormones. A total of 81 patients and 79 controls of similar age and sex were included. Demographic, anthropometric, laboratory data, trabecular bone score, bone mineral density, serum 25-hydroxyvitamin D (25OHD), serum amino-terminal pro-peptide of type 1 collagen (PINP), and C-terminal telopeptide of type 1 collagen (CTX) concentrations were assessed in both groups. Patients with HS had lower serum 25OHD levels than controls, and approximately 62% of them had vitamin D deficiency. Serum PINP was increased and CTX was decreased in patients with HS. Fully adjusted trabecular bone score values were lower in patients with HS compared with controls. Adjusted lumbar bone mineral density was similar in HS and controls, whilst total hip bone mineral density was lower in patients with HS. There were no statistical differences regarding disease severity in terms of 25OHD, serum turnover markers, bone mineral density, or trabecular bone score values. This study shows that patients with HS have lower trabecular bone score and total hip bone mineral density values than population-based controls. In addition, the prevalence of vitamin D deficiency is high in subjects with HS