Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi

On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations

We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach by the Burgers' hierarchy and the Calogero-Degasperis-Ibragimov-Shabat hierarchy

From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Current and future technical, economic and environmental feasibility of maize and wheat residues supply for biomass energy application:Illustrated for South Africa

AbstractThis study assessed the feasibility of mobilising maize and wheat residues for large-scale bioenergy applications in South Africa by establishing sustainable residue removal rates and cost of supply based on different production regions. A key objective was to refine the methodology for estimating crop residue harvesting for bioenergy use, while maintaining soil productivity and avoiding displacement of competing residue uses. At current conditions, the sustainable bioenergy potential from maize and wheat residues was estimated to be about 104 PJ. There is potential to increase the amount of crop residues to 238 PJ through measures such as no till cultivation and adopting improved cropping systems. These estimates were based on minimum residues requirements of 2 t ha−1 for soil erosion control and additional residue amounts to maintain 2% SOC level.At the farm gate, crop residues cost between 0.9 and 1.7 $GJ−1. About 96$ GJ−1. In the improved scenario, up to 85% of the biomass is below 1.3 $GJ−1. For biomass deliveries at the conversion plant, about 36$ GJ−1 while in the optimised scenario, about 87% is delivered below 5$ GJ−1. Co-firing residues with coal results in lower cost of electricity compared to other renewables and significant GHG (CO2 eq) emissions reduction (up to 0.72 tons MWh−1). Establishing sustainable crop residue supply systems in South Africa could start by utilising the existing agricultural infrastructure to secure supply and develop a functional market. It would then be necessary to incentivise improvements across the value chain

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

Espécies florestais nativas prioritárias para produção de sementes e mudas no estado do Amapá.

O Brasil assumiu compromisso internacional de restaurar e reflorestar 12 milhões de hectares de florestas até 2030, nas suas Contribuições Nacionalmente Determinadas firmadas no Acordo de Paris. Embora o desmatamento ainda não seja um grande problema para o Amapá, sementes e mudas de espécies nativas possuem grande potencial como produto regional capaz de contribuir para geração de renda complementar das comunidades e agricultores que detém florestas e utilizam esses recursos como meio de vida. Por isso é necessário conhecer a importância ecológica e comercial de espécies nativas, para auxiliar a cadeia de produção de sementes e mudas na região. O objetivo do estudo foi realizar um levantamento de espécies nativas prioritárias no estado do Amapá, avaliando o grau de importância econômica e ambiental dessas espécies

Photon-Neutrino Interactions in Magnetic Field through Neutrino Magnetic Moment

We study the neutrino-photon processes like $\gamma\gamma\to\nu\bar{\nu}$ in the presence of uniform external magnetic field for the case when neutrinos can couple to the electromagnetic field directly through their dipole magnetic moment and obtain the stellar energy loss. The process would be of special relevance in astrophysical situations where standard left-handed neutrinos are trapped and the right handed neutrinos produced through the spin flip interaction induced by neutrino magnetic moment alone can freely stream out.Comment: LaTex2e file, 9 page

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

gamma nu -> gamma gamma nu and crossed processes at energies below m_W

The cross sections for the processes $\gamma \nu\to \gamma \gamma \nu$, $\gamma\gamma\to\gamma\nu\bar{\nu}$ and $\nu\bar{\nu}\to\gamma\gamma\gamma$ are calculated for a range of center of mass energies from below $m_e$ to considerably above $m_e$, but much less than $m_W$. This enables us to treat the neutrino--electron coupling as a four--Fermi interaction and results in amplitudes which are electron box diagrams with three real photons and one virtual photon at their vertices. These calculations extend our previous low--energy effective interaction results to higher energies and enable us to determine where the effective theory is reliable.Comment: 12 pages, RevTex, 10 postscript figures include