A basic definition of spin in the new matrix dynamics

We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics, and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection.

Integrating Phenological, Aerobiological and Weather Data to Study the Local and Regional Flowering Dynamics of Four Grapevine Cultivars

Phenological, aerobiological, and weather data are useful tools to study local and regional flowering dynamics in crops with economic importance. The present study focuses on four autochthonous grapevine cultivars, namely, ‘Treixadura’, ‘Godello’, ‘Loureira’, and ‘Albariño’ (Vitis vinifera L.), which belong to the Designation of Origin Ribeiro area (located in northwestern Spain) from 2015–2019. The aims of the work were to (1) compare the airborne pollen concentration in the vineyard collected by two different traps, (2) analyze the influence of the main meteorological variables on cultivar phenology and pollen concentration, and (3) test the contribution of the air masses on pollen concentrations in the vineyard. Phenological development has been assessed twice weekly, according to the Biologische Bundesanstalt, Bundessortenamt und Chemische Industrie (BBCH) scale. Airborne pollen concentrations were monitored by using two traps during stage 6 (flowering), namely, a Hirst volumetric sampler and a Cour passive trap. The bioclimatic conditions affected the duration of flowering, ranging from 11 and 24 days. The highest seasonal pollen integral (SPIn) was registered in 2016 for the Hirst sampler, with 302 pollen, and in 2019 for the Cour trap, with 1,797,765 pollen/m2/day. The main variables affecting pollen concentrations were average temperature during the main pollen season, as well as, temperatures and dew points during the pre-peak period. The relationship between pollen data registered by both traps and the obtained harvest indicate that the Hirst trap may be more suitable for predicting a local production and that the Cour sampler is more appropriate for forecasting regional productions.