Covalently Binding the Photosystem I to Carbon Nanotubes

We present a chemical route to covalently couple the photosystem I (PS I) to carbon nanotubes (CNTs). Small linker molecules are used to connect the PS I to the CNTs. Hybrid systems, consisting of CNTs and the PS I, promise new photo-induced transport phenomena due to the outstanding optoelectronic properties of the robust cyanobacteria membrane protein PS I

SUSY structures, representations and Peter-Weyl theorem for S1∣1S^{1|1}

The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\mathbf C}^{1|1})^\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for $S^{1|1}$

Highest weight Harish-Chandra supermodules and their geometric realizations

In this paper we discuss the highest weight $\frak k_r$-finite representations of the pair $(\frak g_r,\frak k_r)$ consisting of $\frak g_r$, a real form of a complex basic Lie superalgebra of classical type $\frak g$ (${\frak g}\neq A(n,n)$), and the maximal compact subalgebra $\frak k_r$ of $\frak g_{r,0}$, together with their geometric global realizations. These representations occur, as in the ordinary setting, in the superspaces of sections of holomorphic super vector bundles on the associated Hermitian superspaces $G_r/K_r$.Comment: This article contains of part of the material originally posted as arXiv:1503.03828 and arXiv:1511.01420. The rest of the material was posted as arXiv:1801.07181 and will also appear in an enlarged version as subsequent postin

Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincar\'e groups in arbitrary dimension. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre Delign

General covariance violation and the gravitational dark matter. I. Scalar graviton

The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative of such a matter. The Lagrangian formalism for the continuous medium, the perfect fluid in particular, in the scalar graviton environment is developed. The implications for cosmology are shortly indicated.Comment: 11 pages; minor correction

Tetrads in SU(3) X SU(2) X U(1) Yang-Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in four-dimensional Lorentzian spacetimes. In the present manuscript a new tetrad is introduced for the Yang-Mills SU(3) X SU(2) X U(1) formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations. New theorems are proved regarding isomorphisms between local internal SU(3) X SU(2) X U(1) groups and local tensor products of spacetime LB1 and LB2 groups of transformations. The new tetrads and the stress-energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang-Mills stress-energy tensor is developed.Comment: There is a new appendix. The unitary transformations by local SU(2) subgroup elements of a local group coset representative is proved to be a new local group coset representative. This proof is relevant to the study of the memory of the local tetrad SU(3) generated gauge transformations. Therefore, it is also relevant to the group theorems proved in the paper. arXiv admin note: substantial text overlap with arXiv:gr-qc/060204

Extreme phase and rotated quadrature measurements

We determine the extreme points of the convex set of covariant phase observables. Such extremals describe the best phase parameter measurements of laser light - the best in the sense that they are free from classical randomness due to fluctuations in the measuring procedure. We also characterize extreme fuzzy rotated quadratures