Search results for "Mathematica"
showing 10 items of 7971 documents
Mixed microalgae culture for ammonium removal in the absence of phosphorus: Effect of phosphorus supplementation and process modeling
2014
Microalgal growth and ammonium removal in a P-free medium have been studied in two batch photobioreactors seeded with a mixed microalgal culture and operated for 46 days. A significant amount of ammonium (106 mg NH4-Nl(-1)) was removed in a P-free medium, showing that microalgal growth and phosphorus uptake are independent processes. The ammonium removal rate decreased during the experiment, partly due to a decrease in the cellular phosphorus content. After a single phosphate addition in the medium of one of the reactors, intracellular phosphorus content of the corresponding microalgal culture rapidly increased, and so did the ammonium removal rate. These results show how the amount of phos…
Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes
2018
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, $\mathrm{F}\ensuremath{\rightarrow}\mathrm{F}\mathrm{cos}\ensuremath{\theta}+^{\ensuremath{\star}}\mathrm{F}\mathrm{sin}\ensuremath{\theta}$. These transformations are indeed a symmetry of the theory in the Noether sense. The associated constant of motion is the difference in the intensity between self-dual and anti-self-dual components of the electromagnetic field or, equivalently, the difference between the right and left circularly polarized components. This conservation law holds even if the electromagnetic field interacts with an arbitrary classical gravitational background.…
CHIRAL ANOMALY IN ASHTEKAR'S APPROACH TO CANONICAL GRAVITY
1998
The Dirac equation in Riemann–Cartan spacetimes with torsion is reconsidered. As is well-known, only the axial covector torsion A, a one-form, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin type four-form dA ∧ dA does arise additionally in the chiral anomaly, but not the Nieh–Yan term d* A, as has been claimed recently. Implications for cosmic strings in Einstein–Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.
Chiral anomalies in even and odd dimensions
1985
Odd dimensional Yang-Mills theories with an extra ‘topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.
Chiral expansion of the nucleon mass to order q^6
2006
We present the results of a complete two-loop calculation at order q^6 of the nucleon mass in manifestly Lorentz-invariant chiral perturbation theory. The renormalization is performed using the reformulated infrared renormalization, which allows for the treatment of two-loop integrals while preserving all relevant symmetries, in particular chiral symmetry.
In-medium pi-pi Correlation Induced by Partial Restoration of Chiral Symmetry
2000
We show that both the linear and the non-linear chiral models give an enhancement of the pi-pi cross section near the 2pi threshold in the scalar-iso-scalar (I=J=0) channel in nuclear matter. The reduction of the chiral condensate, i.e., the partial chiral restoration in nuclear matter, is responsible for the enhancement in both cases. We extract an effective 4pi-nucleon vertex which is responsible for the enhancement but has not been considered in the non-liear models for in-medium pi-pi interaction. Relation of this vertex and a next-to-leading order terms in the heavy-baryon chiral lagrangian, L_piN^(2), is also discussed.
The Chiral Anomaly
1989
The Dirac operator on a manifold M is a first order partial differential operator acting on sections of a spin bundle over M. The Dirac operator is elliptic when the metric of M is positive definite. The main task in this chapter is to study properties of the determinant of the Dirac operator.
Form factors of the isovector scalar current and the ηπ scattering phase shifts
2015
33 pages.- 14 figures.- v2: Some clarifications and corrections of typos
Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: The subtraction function and moments of unpolarized structur…
2020
The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of low-energy VVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarized VVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the corresponding structure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted, where possible, with "data-driven" dispersive evaluations of low-energy structure quantities, such as nucleon polarizabilities. We find significant dis…
Implementation of local chiral interactions in the hyperspherical harmonics formalism
2021
With the goal of using chiral interactions at various orders to explore properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obta…