Schrödinger representation and Casimir effect in renormalizable quantum field theory

Effective description of brane terms in extra dimensions

“…The tree graphs will have in general new thin-brane singularities, which can be subtracted with analytical renormalization. odd-odd terms appear too, and can be treated as discussed above 6 . In [6,7] complete quantum computations in renormalizable field theories of dimension 4 with boundaries have been performed, and the corresponding renormalization group equations have been studied.…”

“…odd-odd terms appear too, and can be treated as discussed above 6 . In [6,7] complete quantum computations in renormalizable field theories of dimension 4 with boundaries have been performed, and the corresponding renormalization group equations have been studied. The techniques in these references can be applied to theories of dimension higher than 4, although in this case the singularities will be more severe and more counterterms will be required because of non-renormalizability.…”

“…In our perturbative effective framework, the quantum divergences should also be treated in a mass-independent renormalization scheme, such as dimensional regularization with minimal subtraction, so that the renormalization scale µ only appears inside logarithms, and does not interfere with the counting of powers of Λ. In this case, the localized quantum divergences are proportional to exact delta functions and can be cancelled by brane counterterms in the effective theory with vanishing brane width [6,7,8] (for examples showing the smooth profile of divergences with a hard cutoff, see [48,52]). The thin-brane divergences, on the other hand, which appear typically in one-particle reducible (sub)diagrams, can be subtracted using our prescription.…”

Model of Dirac field interacting with material plane within Symanzik’s approach

“…Here Γ is a subspace of dimension D ≤ D in a D-dimensional space [8]. The basic principles of QEDgauge invariance, locality, and renormalizability-impose strong constraints on the possible form of the defect action S de f .…”

“…The results presented in our paper were obtained within the Symanzik's approach [8], in which the interaction of quantized fields with a spatial inhomogeneity is modeled by an additional action functional (defect action), concentrated in the spatial domain where this inhomogeneity -a macroscopic object -is located. An important assumption is also that the standard requirements for quantum field models (locality, renormalizability, symmetry properties) are fulfilled.…”