Particle Pair Production in Cosmological General Relativity

The Cosmological General Relativity (CGR) of Carmeli, a 5-dimensional (5-D) theory of time, space and velocity, predicts the existence of an acceleration a_0 = c / tau due to the expansion of the universe, where c is the speed of light in vacuum, tau = 1 / h is the Hubble-Carmeli time constant, where h is the Hubble constant at zero distance and no gravity. The Carmeli force on a particle of mass m is F_c = m a_0, a fifth force in nature. In CGR, the effective mass density rho_eff = rho - rho_c, where rho is the matter density and rho_c is the critical mass density which we identify with the vacuum mass density rho_vac = -rho_c. The fields resulting from the weak field solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a pair of particles. The mass of each particle is found to be m = tau c^3 / 4 G, where G is Newton's constant. The vacuum mass density derived from the physics is rho_vac = -rho_c = -3 / (8 pi G tau^2). The cosmic microwave background (CMB) black body radiation at the temperature T_o = 2.72548 K which fills that volume is found to have a relationship to the ionization energy of the Hydrogen atom. Define the radiation energy epsilon_gamma = (1 - g) m c^2 / N_gamma, where (1-g) is the fraction of the initial energy m c^2 which converts to photons, g is a function of the baryon density parameter Omega_b and N_gamma is the total number of photons in the CMB radiation field. We make the connection with the ionization energy of the first quantum level of the Hydrogen atom by the hypothesis epsilon_gamma = [(1 - g) m c^2] / N_gamma = alpha^2 mu c^2 / 2, where alpha is the fine-structure constant and mu = m_p f / (1 + f), where f= m_e / m_p with m_e the electron mass and m_p the proton mass.Comment: 14 pages, 0 figures. The final publication is available at springerlink.co

Cosmological Relativity: A General-Relativistic Theory for the Accelerating Expanding Universe

Recent observations of distant supernovae imply, in defiance of expectations, that the universe growth is accelerating, contrary to what has always been assumed that the expansion is slowing down due to gravity. In this paper a general-relativistic cosmological theory that gives a direct relationship between distances and redshifts in an expanding universe is presented. The theory is actually a generalization of Hubble's law taking gravity into account by means of Einstein's theory of general relativity. The theory predicts that the universe can have three phases of expansion, decelerating, constant and accelerating, but it is shown that at present the first two cases are excluded, although in the past it had experienced them. Our theory shows that the universe now is definitely in the stage of accelerating expansion, confirming the recent experimental results

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

Carmeli's accelerating universe is spatially flat without dark matter

Carmeli's 5D brane cosmology has been applied to the expanding accelerating universe and it has been found that the distance redshift relation will fit the data of the high-z supernova teams without the need for dark matter. Also the vacuum energy contribution to gravity indicates that the universe is asymptotically expanding towards a spatially flat state, where the total mass/energy density tends to unity.Comment: 4 pages, 5 figures, accepted for publication in Int. J. Theor. Physics, this paper is based on an invited talk at FFP6, Udine, Italy, Sept 200

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

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 $S^{1|1}$

Tetrads in Geometrodynamics

A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the electromagnetic field. The Einstein-Maxwell equations will also be simplified

Commutative POVMs and Fuzzy Observables

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.Comment: Contribution to the Pekka Lahti Festschrif

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