New equation for a spin 1/2 particle with three additional characteristics in presence of electromagnetic and gravitational fields

Fradkin’s model for a spin-3/2 particle in the presence of external fields is investigated. Applying the general Gel’fand–Yaglom formalism, we develop this model on the base of a set of six irreducible representations of the proper Lorentz group, making up a 20-component wave function. Applying the standard requirements such as the relativistic invariance, single nonzero mass, spin S =3/2, P-symmetry, and existence of a Lagrangian for the model, we derive a set of spinor equations, firstly in the absence of external fields. The 20-component wave function consists of a bispinor and a vector-bispinor. In the absence of external fields, the Fradkin model reduces to the minimal Pauli–Fierz (or Rarita–Schwinger) theory. Details of this equivalence are given. Then we take the presence of external electromagnetic fields into account. It turns out that the Fradkin equation in the minimal form contains an additional interaction term governed by electromagnetic tensor Fab. In addition, we consider the external curved space-time background. In the generally covariant case, the Fradkin equation contains the additional gravitational interaction term governed by the Ricci tensor Rab. If the electric charge of a particle is zero, the Fradkin model remains correct and describes a neutral Majorana-type spin-3/2 particle interacting additionally with the geometric background through the Ricci tensor.

Effect of interconvertibility of electromagnetic and gravitational waves in strong external electromagnetic fields and the propagation of waves in the field of a charged “black hole”: PMM vol. 38, n≗ 6, 1974, pp. 1122–1129

The quantum fluctuations of the Dirac field in external classical gravitational and electromagnetic fields are studied. A self-consistent equation for torsion is calculated, which is obtained using one-loop fermion diagrams.

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a “charged” fermion in a external field characterized by a certain “3-pseudo-vector potential.” The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.

In the frames of general formalism by Gel’fand–Yaglom, starting with an extended set of representations of the Lorentz group, we have constructed relativistic equation for a spin 1/2 particle with two additional electromagnetic characteristics. We take into account the presence of external electromagnetic fields. After eliminating the supplementary variables of the complete wave function we have derived a generalized Dirac-like equation, which includes two additional interaction terms, they are related to anomalous magnetic moment and polarizability.

Herein, a spin 1 particle with anomalous magnetic moment in an external Coulomb field is studied. We start with the relativistic tensor system of the Proca type in Cartesian coordinates. In these equations the Γ parameter is present related to an additional characteristic of the particle. In the case of an external magnetic field, it is interpreted as an anomalous magnetic moment. In the presence of an external electric field, additional interaction terms are presented as well; moreover, the terms of the first and second orders in parameter Γ appear. The case of an external Coulomb field is considered in detail. In the nonrelativistic approximation a Pauli type equation is obtained. In the nonrelativistic equation the separation of the variables with the use of spherical vectors is realized. One separate 2-nd order differential equation is found, in which additional interaction terms are missing. Besides, we derive systems of two coupled 2-nd order equations wherein linear and quadratic in parameter Γ interaction terms are presented. Previously, another approach was developed for analyzing the vector particle with anomalous magnetic moment. It was based on the use of tetrad formalism and separation of the variables in the Duffin – Kemmer equation with the help of the Wigner function. The nonrelativistic approximation was performed directly in the system of radial equations. Besides, previously formal Frobenius type solutions for an arising 4-th order differential equation were constructed; however, physically interpretable energy spectra were not found. We have proved that the radial equations derived by different methods are the same up to a simple liner transformation over two radial functions. In this paper, we have obtained a simpler 4-th order equation, the construction of Frobenius solutions becomes technically easier, but physical energy spectra are not found either.

Effect of external electromagnetic field and bias voltage on the vapor growth, morphology and properties of carbon micro coils

We fulfill the detailed analysis of coupling the charged bosonic higher-spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic higher-spin fields with external field is found. Construction is based on deformation of free Lagrangian and free gauge transformations by terms linear in electromagnetic field strength. In massive case a formulation with Stueckelberg fields is used. We begin with the most general form of deformations for Lagrangian and gauge transformations, admissible by Lorentz covariance and gauge invariance and containing some number of arbitrary coefficients, and require the gauge invariance of the deformed theory in first order in strength. It yields the equations for the coefficients which are exactly solved. As a result, the complete interacting Lagrangian of arbitrary bosonic higher-spin fields with constant electromagnetic field in first order in electromagnetic strength is obtained. Causality of massive spin-2 and spin-3 fields propagation in the corresponding electromagnetic background is proved.

For pt.I, see ibid., vol.8, p.515 (1991). Using Maslov's complex sprout method, special classes of the Ehrenfest-type approximate solutions of the Dirac equation in curved spacetime in the presence of external electromagnetic and torsion fields are constructed. They form a complete orthonormalized set of quasiclassical trajectory-coherent one-particle quantum states (TCS) and are strongly peaked around the worldline neighbourhood of the charged particle. The key tool in the TCS construction is the ' gamma -reconstruction' technique with the help of which it can be shown that the problem of TCS construction is reduced to the solution of the linear evolution equation for a two-component spinor. On the basis of the results obtained the generally covariant spinning equation of motion in the case of background gravitational, electromagnetic and torsion fields is deduced from the Dirac equation.

This paper investigates the nonrelativistic approximation in the first-order 39- component theory for a spin-3/2 particle in curved spacetime under external electromagnetic fields. Starting from the generally covariant matrix equations, generalized via the Weyl-Fock- Ivanenko tetrad method, we employ explicit forms of the four main Γa matrices of dimension 1616 within the corresponding first-order system. The analysis is carried out for spacetime metrics that permit the existence of nonrelativistic equations. To separate the large and small components of the complete wave function, three projective operators are constructed from the fourth-order minimal polynomial of the 1616 Γ0 matrix. The explicit forms of these components are obtained, and the set of independent variables is identified; in particular, only four large components are independent. Following the standard procedure, we derive the nonrelativistic system of equations for a 4-component wave function. The resulting Hamiltonian includes contributions from the electromagnetic field and additional geometric terms expressed through the Ricci rotation coefficients, Ricci scalar R and Ricci tensor Rab . We also isolate the term describing the interaction between the magnetic moment of the spin-3/2 particle and the external magnetic field. This interaction term is expressed via the spin matrices Si and the components of the magnetic field vector B.

Energy of a classical charged particle in an external electromagnetic field

Nonequilibrium molecular dynamics (NMD) simulations are performed to investigate the effects of an external electromagnetic (E/M) field on NaCl electrolyte solutions at different temperatures using the SPC/E model. The electromagnetic wave propagates in the z-axis direction with a frequency of 2.45 GHz, and the intensity of the E/M field is 3 x 10(4) V/m. The results indicate that as the concentration of the electrolyte solution increased, the diffusion coefficient and the ionic mobility gradually decreased, but the electric conductivity gradually increased. In addition, all three of them will be increased when the temperature is increased. But their value will be reduced when the electromagnetic field is applied.

Electromagnetic fields (EMFs) are ever-present, and so is the need to better understand their influence on human health and biological matter in general. The interaction between a molecular system and external EMF can alter the structure, and dynamical behaviour, and, hence, biological function of proteins with uncertain health consequences. This urges a detailed investigation of EMF-induced effects on basic protein biophysics. Here, we used all-atom non-equilibrium molecular dynamics simulations to understand and quantify the response mechanisms of the amyloidogenic apoC-II(60-70) peptides to non-ionising radiation by modelling their behaviour under external electromagnetic and electric fields of different strengths. Our simulations show high strength fields (>0.04 V/nm) cause structural changes in apoC-II(60-70) due to the peptide dipole alignment along the applied field direction, which disrupts the inherent β-hairpin conformation known to be the intermediate state for fibril formation. The intermediate field-strength range (0.04-0.004 V/nm) causes a significant acceleration in peptide dynamics, which leads to the increased population of structures with fibril-inhibiting characteristics, such as the separated N- and C-termini and colocation of the aromatic residues at the same peptide face. In contrast, lower field strengths (<0.004 V/nm) promote the formation of the amyloid-prone hairpin structures relative to the ambient conditions. These findings suggest that intermediate-strength electromagnetic fields could be considered for designing alternative treatments of amyloid diseases, while the very high and low field strengths could be employed for engineering well-ordered fibrillar aggregates for non-medicinal applications.

Nonequilibrium molecular-dynamics (MD) simulations have been performed for the growth and dissolution of a spherical methane hydrate crystallite, surrounded by a saturated water-methane liquid phase, in both the absence and presence of external electromagnetic (e/m) fields in the microwave to far infrared range (5-7500 GHz) at root-mean square (rms) electric field intensities of up to 0.2 V/A. A rigid/polarizable potential was used to model water and a rigid/nonpolarizable model was utilized for methane. In the absence of a field, it was found that the average growth rate of the crystallite was approximately 0.32 water and 0.045 methane molecules per picosecond, evaluated over a 500 ps NPT simulation for three different initial geometries. Upon the application of an e/m field, it was found that no significant deviations from the zero-field crystal growth patterns were observed for rms electric field intensities of less than about 0.1 V/A, regardless of the field frequency. At, and above, this "threshold" intensity, it was found that dissolution took place. The mobility of the molecules in the system was enhanced by the e/m field, to the greatest extent for frequencies of 50-100 GHz. Furthermore, it was observed that there was a systematic frequency variation in the pattern of dipole alignment with the external field and this led to marked differences in the rate of dissolution.

Calculation of the electric field and potential inside a wire structured object in an external pulse electromagnetic field of a lightning discharge is presented. The conductive structure is solved as a receiving antenna using program SPAN for an arbitrary antenna configuration, consisting of lineic cylindrical segments, in external electromagnetic field. One simple approximation for the external pulse field is used, the parameters of which are calculated for a standard pulse function. The fast Fourier transform (FFT) is performed on this function and antenna response in the time domain is obtained using the inverse fast Fourier transform (IFFT) to the results of the program SPAN in the frequency domain. The results for the electric field and for the potential, as the consequences of induced currents, are presented in the form of graphics.