Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime

A method for computing the stress-energy tensor for the quantized, massless, spin 1/2 field in a general static spherically symmetric spacetime is presented. The field can be in a zero temperature state or a non-zero temperature thermal state. An expression for the full renormalized stress-energy tensor is derived. It consists of a sum of two tensors both of which are conserved. One tensor is written in terms of the modes of the quantized field and has zero trace. In most cases it must be computed numerically. The other tensor does not explicitly depend on the modes and has a trace equal to the trace anomaly. It can be used as an analytic approximation for the stress-energy tensor and is equivalent to other approximations that have been made for the stress-energy tensor of the massless spin 1/2 field in static spherically symmetric spacetimes.Comment: 34 pages, no figure

Paul dirac’s peculiar synthesis of quantum mechanics and special relativity: An intertheoretic context

One of the key episodes of the history of modern physics - Paul Dirac’s 1928 contrivance of the relativistic theory of the electron - in the context of lucid epistemological model of mature theory change is elicited. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s methodology of the General Relativity creation. The structure of Dirac’s scientific research programme and first and foremost the three pivotal principles that put up its heuristics is scrutinized with special emphasis on the “mathematical beauty". It is contended that it was the general relativity genesis elicited in Eddington’s masterpiece “The Mathematical Theory of Relativity" that constituted Dirac’s synthetic paradigm with its emphasis on mathematical speculation, continual modification and generalization of the basic axioms and with the Clifford algebra and Weyl’s bispinors playing the dual lead of Riemannian geometry and Einstein’s metrical tensor. It is punctuated that in spite of the relentless Dirac’s remarks underestimating the role of philosophy one can trace its indirect influence through Arthur Eddington’s whimsical philosophy of science grounded on Hermann Weyl’s quasi-Husserlian epistemology. The basic stages of realization of Dirac’s research programme are elicited with a special emphasis on the crossbred (dual) objects’ construction