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Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.


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Journal ArticleDOI
TL;DR: In this article, the authors review the theories that they have used to develop two finite-element software packages, one using a magnetic vector potential combined with an electric scalar potential in conducting regions and only the magnetic vector vector potential elsewhere.
Abstract: The authors review the theories that they have used to develop two finite-element software packages. One uses a magnetic vector potential combined with an electric scalar potential in conducting regions and only the magnetic vector potential elsewhere. The second formulation is based on an electric vector potential and a magnetic scalar potential whereby only the latter is used in conducting regions. A way to obtain unique solutions by satisfying the divergence condition of the vector potentials is shown. Calculations for several problems are reported, showing the efficiency of the codes. The pros and cons of both formulation are discussed. >

34 citations

Journal ArticleDOI
TL;DR: In this paper, a relativistic theory of nuclear forces has been proposed, which is based on the electron-neutrino field and is relativistically invariant for transformations involving low velocities.
Abstract: Cosmic-ray showers indicate that at high energies interaction between nuclear particles is concerned with the creation and destruction of matter. It may, therefore, be expected that a complete relativistic theory of nuclear forces will involve explicit reference to the phenomena described at present as the electron-neutrino field. Theories of this kind are still too incomplete and self-contradictory to be reliable in practical work. It is, nevertheless, possible to set up equations which are relativistically invariant for transformations involving low velocities. Such equations form the subject of the present report. They are restricted to energies of relative motion that are small in comparison with the rest mass. By means of them it should be possible to discuss relativistic effects for ordinary nuclear energy levels. Possible forms of classical equations contain an interaction energy between two particles in the form given by Eq. (13.2). Here $a$, $b$ are arbitrary real constants. The vector from particle 1 to particle 2 is r, the velocities of the particles are ${\mathrm{v}}_{1}$, ${\mathrm{v}}_{2}$, the velocity of light is $c$. If $a=b=1$, one obtains a generalization of Darwin's equation, which describes the motion of electrically charged particles. For $a=\ensuremath{-}1$, $b=1$ particle 1 acts on particle 2 approximately as though it produced a scalar potential field responsible for the acceleration of particle 2. The requirement of invariance for wave equations of particles with spin (Pauli types) makes it necessary to have spin-orbit coupling which should give rise to the fine structure of nuclear levels. For ordinary interactions the spin-orbit energy may have the form given by Eq. (15.4), where $b$ is an arbitrary real constant, p is the momentum and $\mathbf{\ensuremath{\sigma}}$ is Pauli's spin matrix. For ${b}_{\mathrm{ij}}=\ensuremath{-}1$ one obtains the type of coupling taking place between extranuclear electrons. If ${b}_{\mathrm{ij}}=1$ each particle interacts only with its own orbit as though it were moving in a scalar field. It is the latter hypothesis that is simplest and corresponds to $a=\ensuremath{-}1$, $b=1$ of the classical equation. Extensions of the above classifications have been made to the Majorana [Eqs. (15.7), (15.8)] and the Heisenberg [Eq. (15.9)] ex change interactions. The simplest type in the Majorana case appears to be in satisfactory agreement with experiment for ${\mathrm{Li}}^{7}$ and agrees in order of magnitude with other cases. Extensions to Dirac's types of equations have been made. They lead one to expect coupling between spins of nuclear particles in apparent qualitative but not quantitative agreement with experiment for the deuteron. This agreement is not sufficiently good to establish a form of interaction energy but indicates a possibility of doing so in the future.

34 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that the inclusion of an extremely small quartic coupling constant in the potential for a nearly massless scalar field greatly increases the experimentally allowed region for the mass term and the coupling of the field to matter.
Abstract: We show that inclusion of an extremely small quartic coupling constant in the potential for a nearly massless scalar field greatly increases the experimentally allowed region for the mass term and the coupling of the field to matter

34 citations

Journal ArticleDOI
D. M. Ghilencea1
TL;DR: In this article, a comparative study of Weyl and Palatini theories of quadratic gravity with scale symmetry is presented, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the Weyl action.
Abstract: We present a comparative study of inflation in two theories of quadratic gravity with {\it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_\mu$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_\mu$), Planck scale and metricity emerge in the broken phase after $w_\mu$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($\phi_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($r\sim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($\xi_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $\xi_1\leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.

33 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV), which is severely excluded by the tests of the equivalence principle.
Abstract: The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. The local maximum of the Higgs potential at the symmetric point also contradicts with the conjecture. In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, $Q$, which couples to the cosmological constant and the local maximum of the Higgs potential. In this paper, we show that such a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV). The $Q$-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.

33 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202238
2021137
2020149
2019147
2018147