On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm

A simple derivation of a meaningful, manifestly covariant inner product for real Klein-Gordon (KG) fields with positive semi-definite norm is provided which turns out - assuming a symmetric bilinear form - to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric Quantum Mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.Comment: 8 pages, no figures; correction of obvious typos and marginal improvement of formulation

Kurt Symanzik - a stable fixed point beyond triviality

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.Comment: 6 pages, no figures, new style files, revised for typos, improved discussion, new references adde

NJL with eight quark interactions: Chiral phases at finite T

The thermodynamic potential and thermal dependence of low lying mass spectra of scalars and pseudoscalars are evaluated in a generalized Nambu -- Jona-Lasinio model, which incorporates eight-quark interactions. These are necessary to stabilize the scalar effective potential for the light and strange quark flavors, which would be otherwise unbounded from below. In addition it turns out that they are also crucial to i) lower the temperature of the chiral transition, in conformity with lattice calculations, ii) sharpen the temperature interval in which the crossover occurs, iii) or even allow for first order transitions to occur with realistic quark mass values, from certain critical values of the parameters. These are unprecedented results which cannot be obtained within the NJL approaches restricted to quartic and six-quark interactions.Comment: 6 pages, 3 figures, Talk presented at SCADRON 70 Workshop on Scalar Mesons and Related Topics, Lisbon, 11-16 February 200

Impact of excess NOx emissions from diesel cars on air quality, public health and eutrophication in Europe

Diesel cars have been emitting four to seven times more NOx in on-road driving than in type approval tests. These ‘excess emissions’ are a consequence of deliberate design of the vehicle’s after-treatment system, as investigations during the ‘Dieselgate’ scandal have revealed. Here we calculate health and environmental impacts of these excess NOx emissions in all European countries for the year 2013. We use national emissions reported officially under the UNECE Convention for Long-range Transport of Atmospheric Pollutants and employ the EMEP MSC-W Chemistry Transport Model and the GAINS Integrated Assessment Model to determine atmospheric concentrations and resulting impacts. We compare with impacts from hypothetical emissions where light duty diesel vehicles are assumed to emit only as much as their respective type approval limit value or as little as petrol cars of the same age. Excess NO2 concentrations can also have direct health impacts, but these overlap with the impacts from particulate matter (PM) and are not included here. We estimate that almost 10 000 premature deaths from PM2.5 and ozone in the adult population (age >30 years) can be attributed to the NOx emissions from diesel cars and light commercial vehicles in EU28 plus Norway and Switzerland in 2013. About 50% of these could have been avoided if diesel limits had been achieved also in on-road driving; and had diesel cars emitted as little NOx as petrol cars, 80% of these premature deaths could have been avoided. Ecosystem eutrophication impacts (critical load exceedances) from the same diesel vehicles would also have been reduced at similar rates as for the health effects

Phenomenology of pp->pp eta reaction close to threshold

The recent high statistics measurement of the pp -> pp eta reaction at an excess energy Q=15.5 MeV has been analysed by means of partial wave decomposition of the cross section. Guided by the dominance of the final state 1S0 pp interaction (FSI), we keep only terms involving the FSI enhancement factor. The measured p-p and p-eta effective mass spectra can be well reproduced by lifting the standard on-shell approximation in the enhancement factor and by allowing for a linear energy dependence in the leading 3P0->1S0,s partial wave amplitude. Higher partial waves seem to play only a marginal role

General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space

In our previous work, we proposed a mathematical framework for PT-symmetric quantum theory, and in particular constructed a Krein space in which PT-symmetric operators would naturally act. In this work, we explore and discuss various general consequences and aspects of the theory defined in the Krein space, not only spectral property and PT symmetry breaking but also several issues, crucial for the theory to be physically acceptable, such as time evolution of state vectors, probability interpretation, uncertainty relation, classical-quantum correspondence, completeness, existence of a basis, and so on. In particular, we show that for a given real classical system we can always construct the corresponding PT-symmetric quantum system, which indicates that PT-symmetric theory in the Krein space is another quantization scheme rather than a generalization of the traditional Hermitian one in the Hilbert space. We propose a postulate for an operator to be a physical observable in the framework.Comment: 32 pages, no figures; explanation, discussion and references adde

New Quasi-Exactly Solvable Sextic Polynomial Potentials

A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial potentials is constructed. These new Hamiltonians are different from the sextic QES Hamiltonians in the literature because their eigenfunctions obey PT-symmetric rather than Hermitian boundary conditions. These new Hamiltonians present a novel problem that is not encountered when the Hamiltonian is Hermitian: It is necessary to distinguish between the parametric region of unbroken PT symmetry, in which all of the eigenvalues are real, and the region of broken PT symmetry, in which some of the eigenvalues are complex. The precise location of the boundary between these two regions is determined numerically using extrapolation techniques and analytically using WKB analysis

Images in Christmas Balls

We describe light-reflection properties of spherically curved mirrors, like balls in the Christmas tree. In particular, we study the position of the image which is formed somewhere beyond the surface of a spherical mirror, when an eye observes the image of a pointlike light source. The considered problem, originally posed by Abu Ali Hasan Ibn al-Haitham -- alias Alhazen -- more than a millennium ago, turned out to have the now well known analytic solution of a biquadratic equation, being still of great relevance, e.g. for the aberration-free construction of telescopes. We do not attempt to perform an exhaustive survey of the rich historical and engineering literature on the subject, but develop a simple pedagogical approach to the issue, which we believe to be of continuing interest in view of its maltreating in many high-school textbooks.Comment: 13 pages, 7 figures plain LaTeX; Also see http://cft.fis.uc.pt/eef/mirrors.htm, revised version has simplified formulas, more transparent for a wider audience, one reference adde

Modelling street level PM10 concentrations across Europe: source apportionment and possible futures

Despite increasing emission controls, particulate matter (PM) has remained a critical issue for European air quality in recent years. The various sources of PM, both from primary particulate emissions as well as secondary formation from precursor gases, make this a complex problem to tackle. In order to allow for credible predictions of future concentrations under policy assumptions, a modelling approach is needed that considers all chemical processes and spatial dimensions involved, from long-range transport of pollution to local emissions in street canyons. Here we describe a modelling scheme which has been implemented in the GAINS integrated assessment model to assess compliance with PM10 (PM with aerodynamic diameter <10 um) limit values at individual air quality monitoring stations reporting to the AirBase database. The modelling approach relies on a combination of bottom up modelling of emissions, simplified atmospheric chemistry and dispersion calculations, and a traffic increment calculation wherever applicable. At each monitoring station fulfilling a few data coverage criteria, measured concentrations in the base year 2009 are explained to the extent possible and then modelled for the past and future. More than 1850 monitoring stations are covered, including more than 300 traffic stations and 80% of the stations which exceeded the EU air quality limit values in 2009. As a validation, we compare modelled trends in the period 2000-2008 to observations, which are well reproduced. The modelling scheme is applied here to quantify explicitly source contributions to ambient concentrations at several critical monitoring stations, displaying the differences in spatial origin and chemical composition of urban roadside PM10 across Europe. Furthermore, we analyse the predicted evolution of PM10 concentrations in the European Union until 2030 under different policy scenarios. Significant improvements in ambient PM10 concentrations are expected assuming successful implementation of already agreed legislation; however, these will not be large enough to ensure attainment of PM10 limit values in hot spot locations such as Southern Poland and major European cities. Remaining issues are largely eliminated in a scenario applying the best available emission control technologies to the maximal technically feasible extent