An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples

This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our construction applies equally well to Hermitian Hamiltonians which form a subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian matrix Hamiltonians we construct the positive inner product (in the case of $2\times 2$ matrices for both real as well as complex eigenvalues). When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues). We illustrate how this general formalism works out in practice by calculating the inner product for a couple of ${\cal PT}$ symmetric quantum mechanical theories.Comment: 9 pages, revte

Invisible Higgs boson, continuous mass fields and unHiggs mechanism

We explore the consequences of an electroweak symmetry breaking sector which exhibits approximately scale invariant dynamics -- i.e., nontrivial fixed point behavior, as in unparticle models. One can think of an unHiggs as a composite Higgs boson with a continuous mass distribution. We find it convenient to represent the unHiggs in terms of a Kallen-Lehmann spectral function, from which it is simple to verify the generation of gauge boson and fermion masses, and unitarization of WW scattering. We show that a spectral function with broad support, which corresponds to approximate fixed point behavior over an extended range of energy, can lead to an effectively invisible Higgs particle, whose decays at LEP or LHC could be obscured by background.Comment: 8 page

On the Summation of Feynman Graphs

A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increas- ing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon's wavefunction renormalization constant Z3. This analysis provides a qualitative understanding of why the measured value of the renormalized fine structure constant is, approximately, 1/137

Supersymmetric Corrections to the Threshold Production of Top Quark Pairs

In this paper we investigate supersymmetric effects to the threshold production cross section of top quark pairs in electron positron annihilation. In particular, we consider the complete one-loop corrections from the strong and weak sector of the Minimal Supersymmetric Standard Model.Comment: 18 pages, 7 figure

Amplitude Zeroes in Collinear Processes or What Is Left from a Factorizable 2d Model in Higher Dimensions

We show that for collinear processes, i.e. processes where the incoming and outgoing momenta are aligned along the same line, the S-matrix of the tree level 2+1 dimensional Thirring model factorizes: any S - matrix element is a product of $2\rightarrow 2$ elements. In particular this means nullification of all collinear $2 \rightarrow n$ amplitudes for $n > 2$.Comment: latex , 8 pp., 2 fig. not include

Properties of the Scale Invariant O(g4)O(g^4) Lipatov Kernel

We study the scale-invariant $O(g^4)$ kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle $t$-channel unitarity. We detail the variety of Ward identity constraints and infra-red cancellations that characterize its infrared behaviour. We give an analytic form for the full non-forward kernel. For the forward kernel controlling parton evolution at small-x, we give an impact parameter representation, derive the eigenvalue spectrum, and demonstrate a holomorphic factorisation property related to conformal invariance. The results show that, at next-to-leading-order, the transverse momentum infra-red region may produce a strong reduction of the BFKL small-x behavior.Comment: 41 pages in latex, 16 figs. in a uu-encoded ps-fil

Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions

We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension. First, we consider a simple example of $N$-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with $N_f$ fermions. In the latter case, due to self-interaction of non-Abelian fields the proposed recipe requires some modification which, however, does not change the main results. The resulting effective coupling is dimensionless and is running in accordance with the usual RG equations. The corresponding beta function is calculated in the leading order and is nonpolynomial in effective coupling. It exhibits either UV asymptotically free or IR free behaviour depending on the dimension of space-time. The original dimensionful coupling plays a role of a mass and is also logarithmically renormalized. We analyze also the analytical properties of a resulting theory and demonstrate that in general it acquires several ghost states with negative and/or complex masses. In the former case, the ghost state can be removed by a proper choice of the coupling. As for the states with complex conjugated masses, their contribution to physical amplitudes cancels so that the theory appears to be unitary.Comment: 32 pages, 20 figure

Lamb shift in muonic deuterium atom

We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.Comment: 24 pages, 11 figures. arXiv admin note: text overlap with arXiv:hep-ph/061229

Lamb Shift in Muonic Hydrogen

The Lamb shift in muonic hydrogen continues to be a subject of experimental and theoretical investigation. Here my older work on the subject is updated to provide a complementary calculation of the energies of the 2p-2s transitions in muonic hydrogen.Comment: 15 pages, no figures. 2 small misprints corrected. Published in Phys. Rev.

Combined Oxides of Iron, Manganese and Silica as Oxygen Carriers for Chemical-Looping Combustion

Spray-dried particles with the chemical compositions of Fe0.66Mn1.33SiO3 and FeMnSiO3 have been examined as oxygen carrier materials for chemical-looping combustion. The performance of the materials was examined in oxygen release experiments and during fuel operation with natural gas and syngas. The experiments were carried out in a fluidized-bed chemical-looping reactor system designed for a thermal power of 300 W. The reactor system includes an air reactor and a fuel reactor, as well as loop seals and means for circulation of the oxygen carrier particles. Both materials were able to release gas phase oxygen in inert atmosphere at temperatures between 800-950°C, and with approximately equal oxygen concentrations. Fe0.66Mn1.33SiO3 provided higher conversion of natural gas as compared to FeMnSiO3 and the fuel conversion increased with temperature for both materials. During natural gas operation with Fe0.66Mn1.33SiO3 the conversion reached 100% at around 950°C with a fuel reactor inventory of 235 kg/MW. The fuel conversion was improved when the solids inventory was increased; this improvement could especially be observed for FeMnSiO3 as the fuel conversion was lower for this material. Fe0.66Mn1.33SiO3 provided higher fuel conversion than FeMnSiO3 also when syngas was used as fuel. The fuel conversion increased with temperature for both materials and full conversion was reached above 800°C with a fuel reactor inventory of 225 kg/MW for Fe0.66Mn1.33SiO3, while FeMnSiO3 was incapable of providing full conversion. A rather large elutriation of fines and a significant change in particle size distribution could be observed during operation for both materials. Both materials could work as oxygen carrier for chemical-looping with oxygen uncoupling. Fe0.66Mn1.33SiO3 would be preferred as it has higher conversion of both syngas and natural gas, but the attrition behavior of the material would need to be further investigated