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Noether's Theorem and Symmetry

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ISBN: 9783039282340 9783039282357 Year: Pages: 186 DOI: 10.3390/books978-3-03928-235-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Law
Added to DOAB on : 2020-04-07 23:07:08
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Abstract

In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.

SPIG2018

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ISBN: 9783038978503 9783038978510 Year: Pages: 288 DOI: 10.3390/books978-3-03897-851-0 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General) --- Nuclear Physics
Added to DOAB on : 2019-04-25 16:37:17
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This Special Issue covers a wide range of topics from fundamental studies to applications of ionized gases. It is dedicated to four topics of interest: 1. ATOMIC COLLISION PROCESSES (electron and photon interactions with atomic particles, heavy particle collisions, swarms, and transport phenomena); 2. PARTICLE AND LASER BEAM INTERACTION WITH SOLIDS (atomic collisions in solids, sputtering and deposition, and laser and plasma interactions with surfaces); 3. LOW TEMPERATURE PLASMAS (plasma spectroscopy and other diagnostic methods, gas discharges, and plasma applications and devices); 4. GENERAL PLASMAS (fusion plasmas, astrophysical plasmas, and collective phenomena). This Special Issue of Atoms will highlight the need for continued research on ionized gas physics in different topics ranging from fundamental studies to applications, and will review current investigations.

Keywords

strong-field physics --- attoscience --- bicircular field --- high-order harmonic generation --- above-threshold ionization --- spin-polarized electrons --- capacitively-coupled discharge --- oxygen --- particle-in-cell/Monte Carlo collision --- electron heating --- secondary electron emission --- Large Helical Device (LHD) --- deuterium experiment --- ion temperature of 10 keV --- plasma research --- spectroscopic study --- dispersion interferometer --- modified theories of gravity --- methods: analytical --- methods: numerical --- galaxies: elliptical --- galaxies: fundamental parameters --- non-equilibrium --- collisions --- radiation --- planetary atmospheric entry --- laser matter interaction --- laser-induced breakdown --- plasma --- spectroscopy --- streak camera --- plasma --- spectral lines --- Stark broadening --- oxygen --- silicon --- spectroscopy --- gas discharges --- plasma applications --- databases --- virtual observatory --- cross sections --- rate coefficients --- runway electron --- plasma current --- fusion plasma --- tokamak --- glow discharge --- argon --- nitrogen admixture --- discharge voltage --- diffuse discharge --- constricted discharge --- electrical theory of DBDs --- QV-plot --- instantaneous power --- rainbow scattering --- positron channeling effect --- time-dependent Schrödinger equation --- chiral single wall carbon nanotubes --- black hole physics --- cosmology --- quasar spectroscopy --- cosmological parameters --- ionized gas --- broad line region --- Rydberg atoms --- dynamic instability --- control of atomic states --- Förster resonance --- plasma spectroscopy --- Stark broadening --- plasma diagnostics --- line shape modeling --- Zeeman-Doppler broadening --- Balmer line series --- radiative recombination --- photoacoustic --- photothermal --- inverse problem --- thermal memory --- minimum volume cell --- neural networks --- thermal diffusivity --- conductivity --- linear coefficient of thermal extension --- AGN --- black holes --- gravitational waves --- binary black holes --- quasars --- photodetachment --- magnetically confined fusion --- neutral beam injection --- plasma heating --- optical cavity amplification --- low-energy electrons --- electron–molecule interactions --- astrochemistry --- laboratory plasma --- astrophysical plasma --- fusion plasma --- lasers --- stars --- extragalactic objects --- spectra --- spectroscopy --- scaling laws

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