Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics

We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal-Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Keywords: Segal-Bargmann space, Heisenberg group, coherent states, wavelet transform, reproducing kernel, nilpotent Lie group, monogenic functions, Dirac operator, Clifford algebra, (second) quantization, quantum field theory.Comment: 27 pages; LaTeX2e; no picture

TORNADO1 and TORNADO2 are required for the specification of radial and circumferential pattern in the Arabidopsis root

The cell layers of the Arabidopsis primary root are arranged in a simple radial pattern. The outermost layer is the lateral root cap and lies outside the epidermis that surrounds the ground tissue. The files of epidermal and lateral root cap cells converge on a ring of initials (lateral root cap/epidermis initial) from which the epidermal and lateral root cap tissues of the seedling are derived, once root growth is initiated after germination. Each initial gives rise to a clone of epidermal cells and a clone of lateral root cap cells. These initial divisions in the epidermal/lateral root cap initial are defective in tornado1 (trn1) and trn2 plants indicating a requirement for TRN1 and TRN2 for initial cell function. Furthermore, lateral root cap cells develop in the epidermal position in trn1 and trn2 roots indicating that TRN1 and TRN2 are required for the maintenance of the radial pattern of cell specification in the root. The death of these ectopic lateral root cap cells in the elongation zone (where lateral root cap cells normally die) results in the development of gaps in the epidermis. These observations indicate that TRN1 and TRN2 are required to maintain the distinction between the lateral root cap and epidermis and suggest that lateral root cap fate is the default state. It also suggests that TRN1 and TRN2 repress lateral root cap fate in cells in the epidermal location. Furthermore, the position-dependent pattern of root hair and non-root hair cell differentiation in the epidermis is defective in trn1 and trn2 mutants. Together these results indicate that TRN1 and TRN2 are required for the maintenance of both the radial pattern of tissue differentiation in the root and for the subsequent circumferential pattern within the epidermis

A Case of Urogenital Human Schistosomiasis from a Non-endemic Area

© 2015 Calvo-Cano et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

Isocliny in spinor space and Wilson fermions

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4,0), this parametrization is then applied to the study of Dirac traces occurring in Euclidean lattice quantum field theory within the hopping parameter expansion for Wilson fermions.Comment: 31 pages LaTeX, 2 figure