Probability current in zero-spin relativistic quantum mechanics

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein--Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.Comment: 9 pages, no figures; material presented at the Zim\'anyi School, December 7-11, 2015, Budapest, Hungar

Gyengén nemlokális mechanika = Weakly nonlocal mechanics

1. Objektivitás: Megadtuk a fizikai mennyiségek vonatkoztatási rendszer függetlenségének egy új, a hagyományostól jobb megfogalmazását és elkezdtük az ennek megfelelő egységes kontinuumelemélet kidolgozásást. 2. Relativisztikus folyadékok Gyengén nemlokális anyagtörvényekre nemrelativisztikus esetre kifejlesztett módszerünk relativisztikus általánosításával új belső energiasűrűséget javasoltunk disszipatív relativisztikus folyadékokra és megmutattuk, hogy a mélyebb megalapozáson túlmenően javaslatunk generikusan stabil folyadékelméletet eredményez pusztán termodinamikai feltételekből következően. 3. Klasszikus kontinuumok Kidolgoztuk a véges deformációs mechanika kiterjesztéseként a reológiai hatások és munka alapú képlékenységi feltételeket egységes kezelésére is alkalmas termomechanikai kontinuumelméletet. Ezeknek a vizsgálatoknak az eredményeként új reológiai modellcsaládot kaptunk és az elvi eredményeket összevetettük laboratóriumi kísérletekkel. Egy egyszerűsített esetben az egyenleteket megoldottuk egy alagútnyitási problémára. A lokális egyensúlyon túli, gyengén nemlokális és objektív anyag modellek számos más részproblémáját is tárgyaltuk. 4. Mérnöki alkalmazások A tisztán elméleti, illetve ezeknek kísérleti igazolására és alkalmazására irányuló kutatásaink mellett több kimondottan a mérnöki gyakorlatra vonatkozó kérdést is kutattunk (tönkremeneteli kritériumok érzékenysége, víztartalom hatása a kőzetek szilárdságára, stb..). | 1 Objectivity We have given a new definition of the frame independence of physical quantities that is better than the traditional one and started to elaborate a corresponding unified continuum theory. 2 Relativistic fluids We have generalized our method to construct weakly nonlocal constitutive functions in nonrelativistic continua to the realtivistic case. With the help of the method we have given a new concept of internal energy for dissipative relativistic fluids and proved that the generic stability of the new theory is ensured by the thermodynamic inequalities. 3. Classical continua We have given a unified theory of classical thermomechanic continua for finite deformations, rheological effects and plasticity. A new family of rheological models arised as a result. The theoretical predictions were compared to laboratory experiments and an were applied to a tunnel opening problem. We have treated several problems of weakly nonlocal objective constitutive theories beyond local equilibrium. 4. Engineering applications Beyond the previous theoretical research we have treated several problems of rock mechanics that are directly connected to engineering applications. E.g. the sensitivity of Hoek-Diederich formula for rock mass failure, or the effect of moisture content to rock mass strength

Thomas rotation and Thomas precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.Comment: 20 pages, to appear in Int. J. Theo. Phy

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in \cite{rindler}, is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper \cite{herrera}, however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of \cite{rindler} is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of \cite{rindler}. Along the way we also establish some general properties of {\it rotating reference frames}, which may be of independent interest.Comment: 14 pages, 2 figure

Prevalence of cognitive impairment among Hungarian patients with relapsing-remitting multiple sclerosis and clinically isolated syndrome

Background Cognitive impairment (CI) is a frequent symptom of multiple sclerosis (MS); its prevalence is reported to be 43–70%. It is one of the most important determinants of MS patients’ quality of life, as it is one of the main factors for MS patients becoming unemployed. Aim We aimed to determine the prevalence of CI among the relapsing-remitting MS (RRMS) and clinically isolated syndrome (CIS) patients in Hungary, to evaluate the predicting factors of CI and to assess the differences between sexes and patients with different educational levels. Patients and methods Five-hundred and fifty-three CIS and RRMS patients were enrolled to our study from three Hungarian MS centers. Age at screening, age at disease onset, disease duration, EDSS score, sex and educational levels were analyzed as socio-demographic factors. The BICAMS battery was used to assess their cognitive state, the BDI-II battery to assess depression. For statistical analysis, we utilized logistical regression, and used Fisher exact tests, chi-square tests and one-way ANOVA. Results The mean age of our patients was 44.93 ± 11.69 years, mean age at disease onset was 31.95 ± 10.01 years, the mean disease duration was 13.05 ± 8.05 years and the median EDSS score 2.0 (Range: 6.5, IQR:2.0) points. Three-hundred and sixteen (57.1%) patients had CI. Sex, educational level and EDSS score proved to be significant predictors of CI (OR: 2.71, p < 0.001; OR: 1.94, p = 0.023; OR: 0.47, p = 0.003 respectively). CI was significantly (p < 0.001) more frequent among men (70.1%) than women (52.0%). We found, that educational level and EDSS score were only a significant predicting factor among women. Thus, the prevalence of CI among women with college or university degree was significantly (p < 0.001) less common (39.4%) than women with 12–15 years of education (57.4%) and women without a high school degree (66.7%). Also, we found that among women with higher EDSS score than 2 points, the prevalence of CI is 69.9% as compared to women with EDSS score between 0 and 2 points, where the prevalence is 42.8% (p < 0.001). No such differences were observed among man. Discussion Our prevalence data is similar to those reported in the literature (43–70%), and almost identical to the one assessment using the BICAMS battery. We found that men are more vulnerable to CI than women in MS, as was reported recently. We are the first to report however, that higher educational level and lower EDSS scores are only associated with better cognitive performance in women. © 201