ABSTRACT
The Lorentz-Dirac equation is formulated and studied in flat Minkowski spacetime. A concise, novel derivation of the equation is presented. The problem is then enlarged to study radiation damping of an electron moving through a gravitational field. The equation of motion is obtained for this case as well. It is suggested the study of the problem might motivate experiments which could shed light on the recent work related to the emergence of space-time and its structure by means of quantum effects such as quantum entanglement.
ABSTRACT
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of the space functions as a constant parameter. For a specific metric which defines the manifold, Lie differentiation of the metric gives these symmetries. A metric is used such that the resulting Schrödinger equation can be solved in terms of hypergeometric functions. This permits the investigation of both the energy spectrum and wave functions exactly for this system.
ABSTRACT
No longitudinal study has investigated whether autoantibody titres and serum IgG levels correlate with disease activity in autoimmune liver disease. To determine this, we investigated prospectively 19 patients on 254 occasions between 10 months to 5 years from diagnosis. Nine had anti-nuclear and/or anti-smooth muscle antibody (ANA/SMA) positive autoimmune hepatitis (type 1 AIH), 5 liver kidney microsomal type 1 (LKM-1) positive AIH (type 2 AIH) and 5 ANA/SMA positive autoimmune sclerosing cholangitis (ASC). Correlation between IgG levels, titres of ANA, SMA and LKM-1 and levels of the organ specific autoantibodies anti-liver specific protein (anti-LSP), and anti-asialoglycoprotein receptor (anti-ASGPR) with biochemical evidence of disease activity, as measured by serum aspartate amino transferase (AST) levels, was sought during the course of the disease. AST levels correlated with levels of anti-LSP, anti-ASGPR and IgG in type 1 and 2 AIH, but not in ASC. Positive correlation with AST was also observed for LKM-1 titres in type 2 AIH and for SMA titres in type 1 AIH, but not in ASC. In both AIH and ASC, AST levels correlated with the T cell-dependent immune responses anti rubella IgG and anti tetanus toxoid IgG, but not with the T cell-independent IgG2 response to pneumococcal capsular polysaccaride. Our results indicate that measurement of organ and non-organ specific autoantibodies and IgG levels may be used to monitor disease activity in AIH.
