Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Reading from nowhere: assessed literary response, Practical Criticism and situated cultural literacy

School examinations of student responses to literature often present poetry blind or “unseen”, inviting decontextualised close reading consistent with the orientation-to-text associated with Practical Criticism (originating in the UK) and New Criticism (originating in the USA). The approach survives in the UK after curricular reforms and government have promulgated cultural literacy as foundational for learning. How is cultural literacy manifest in student responses to literature? To what extent can it be reconciled with Practical Criticism where the place of background knowledge in literary reading is negligible? This article explores their uneasy relationship in pedagogy, curricula and assessment for literary study, discussing classroom interactions in England and Northern Ireland where senior students (aged 16–17) of English Literature consider Yeats’ “culture-making” poem “Easter, 1916”. Using methods where teachers withhold contextual information as they elicit students’ responses, the divergent responses of each class appear to arise from differing access to background knowledge according to local though superficially congruent British cultures. The author proposes “situated cultural literacy” to advance the limited application of Practical Criticism in unseen tasks, acknowledge Richards’ original intent, and support the coherence of assessment with curricular arrangements invoking cultural literacy as a unifying principle