scholarly journals On the Majorana Equation: Relations between Its Complex Two-Component and Real Four-Component Eigenfunctions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Eckart Marsch
Keyword(s):  
Dispersion Relation ◽  
Dirac Equation ◽  
Massive Particle ◽  
Mass Term ◽  
Complex Conjugation ◽  
Conjugation Operator ◽  
Direct Linearization ◽  
Two Component ◽  
Relativistic Dispersion ◽  
Component Spinor

We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex conjugation operator and the Pauli spin matrices, corresponding to the irreducible representation of the Lorentz group. Then we derive the complex two-component eigenfunctions of the Majorana equation and the related quantum fields in a concise way, by exploiting the so-called chirality conjugation operator that involves the spin-flip operator. Subsequently, the four-component spinor solutions of the real Majorana equation are derived, and their intrinsic relations with the spinors of the complex two-component version of the Majorana equation are revealed and discussed extensively.

An Analysis of Wave Propagation in Bubbly Two-Component, Two-Phase Flow

1985 ◽  
Vol 107 (2) ◽  
pp. 402-408 ◽  
Author(s):  
L. Y. Cheng ◽  
D. A. Drew ◽  
R. T. Lahey
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Two Phase Flow ◽  
Wave Attenuation ◽  
Bubbly Flow ◽  
Mass Term ◽  
Resonance Phenomenon ◽  
Phase Flow ◽  
Two Phase ◽  
Two Component

Wave propagation in bubbly two-phase, two-component flow was analyzed to assess the validity of some interfacial transfer laws for two-fluid models of two-phase flow. A dispersion relation was derived from the linearized conservation equations and the Rayleigh equation. The phase velocity and wave attenuation calculated from the dispersion relation, compared well with existing high- and low-frequency data. The virtual mass term was found to have a significant effect on wave dispersion in the bubbly flow regime. Thermal effects were found to be important in determining the resonance phenomenon and wave scattering was a major source of damping at frequencies higher than the resonance frequency.

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

scholarly journals A local description of dark energy in terms of classical two-component massive spin-one uncharged fields on spacetimes with torsionful affinities

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Jorge G. Cardoso
Keyword(s):  
Dark Energy ◽  
Physical Properties ◽  
Gauge Group ◽  
Wave Equations ◽  
Wave Functions ◽  
Local Description ◽  
Massive Spin ◽  
Two Component ◽  
Curved Spacetimes ◽  
Component Spinor

AbstractIt is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deriving explicitly the wave equations that supposedly control the propagation in spacetime of the dark energy background. What immediately comes out of this derivation is a presumably natural display of interactions between the fields and both spin torsion and curvatures. The physical properties that may arise directly fromthe solutions to thewave equations are not brought out.

scholarly journals FROM SPINOR GEOMETRY TO COMPLEX GENERAL RELATIVITY

2005 ◽  
Vol 02 (04) ◽  
pp. 675-731 ◽  
Author(s):  
GIAMPIERO ESPOSITO
Keyword(s):  
General Relativity ◽  
Minkowski Space ◽  
Dual Space ◽  
Conformal Gravity ◽  
Penrose Transform ◽  
Minkowski Space Time ◽  
Two Component ◽  
Spinor Geometry ◽  
Complex General Relativity ◽  
Component Spinor

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component spinor calculus, conformal gravity, α-planes in Minkowski space-time, α-surfaces and twistor geometry, anti-self-dual space-times and Penrose transform, spin-3/2 potentials, heaven spaces and heavenly equations.

scholarly journals A Quantum Theory of the Rigid Body in Terms of a Two-Component Spinor

1967 ◽  
Vol 37 (6) ◽  
pp. 1319-1329 ◽  
Author(s):  
Osamu Hara ◽  
Tetsuo Got\=o ◽  
S. Y. Tsai ◽  
Haruichi Yabuki
Keyword(s):  
Quantum Theory ◽  
Rigid Body ◽  
Two Component ◽  
Component Spinor

scholarly journals High-energy positrons and gamma radiation from decaying constituents of a two-component dark atom model

2015 ◽  
Vol 24 (13) ◽  
pp. 1545004 ◽  
Author(s):  
K. Belotsky ◽  
M. Khlopov ◽  
C. Kouvaris ◽  
M. Laletin
Keyword(s):  
Dark Matter ◽  
Massive Particle ◽  
Cosmic Ray ◽  
High Energy ◽  
Photon Flux ◽  
Dark Matter Candidate ◽  
Small Range ◽  
State Radiation ◽  
Two Component ◽  
Doubly Charged

We study a two-component dark matter candidate inspired by the minimal walking technicolor (WTC) model. Dark matter consists of a dominant strongly interactive massive particle (SIMP)-like dark atom component made of bound states between primordial helium nuclei and a doubly charged technilepton and a small WIMP-like component made of another dark atom bound state between a doubly charged technibaryon and a technilepton. This scenario is consistent with direct search experimental findings because the dominant SIMP component interacts too strongly to reach the depths of current detectors with sufficient energy to recoil and the WIMP-like component is too small to cause significant amount of events. In this context, a metastable technibaryon that decays to [Formula: see text], [Formula: see text] and [Formula: see text] can, in principle, explain the observed positron excess by AMS-02 and PAMELA, while being consistent with the photon flux observed by FERMI/LAT. We scan the parameters of the model and we find the best possible fit to the latest experimental data. We find that there is a small range of parameter space that this scenario can be realized under certain conditions regarding the cosmic ray propagation and the final state radiation (FSR). This range of parameters fall inside the region where the current run of large hadron collider (LHC) can probe, and therefore it will soon be possible to either verify or exclude conclusively this model of dark matter.

scholarly journals Nonstandard Dirac equations for nonstandard spinors

2014 ◽  
Vol 23 (14) ◽  
pp. 1444007 ◽  
Author(s):  
A. G. Nikitin
Keyword(s):  
Dirac Equation ◽  
Mass Term ◽  
Charge Conjugation ◽  
Poincaré Group ◽  
Poincare Group ◽  
Dirac Equations ◽  
Generalized Dirac Equation ◽  
Carrier Space ◽  
New Look

Generalized Dirac equation with operator mass term is presented. Its solutions are nonstandard spinors (NSS) which, like eigenspinoren des Ladungskonjugationsoperators (ELKO), are eigenvectors of the charge conjugation and dual-helicity operators. It is demonstrated that in spite of their noncovariant nature the NSS can serve as a carrier space of a representation of Poincaré group. However, the corresponding boost generators are not manifestly covariant and generate nonlocal momentum dependent transformations, which are presented explicitly. These results can present a new look on group-theoretical grounds of ELKO theories.

scholarly journals OBLIQUE CORRECTIONS IN THE MSSM AT ONE LOOP II: FERMIONS

2013 ◽  
Vol 28 (01) ◽  
pp. 1250238 ◽  
Author(s):  
YAO YU ◽  
SIBO ZHENG
Keyword(s):  
Standard Model ◽  
Detailed Analysis ◽  
Gauge Bosons ◽  
Self Energy ◽  
Two Component ◽  
Spinor Formalism ◽  
Component Spinor

This paper is the completion of an earlier work arXiv:1207.4867 which involves the derivation of oblique corrections in the MSSM at one-loop. In terms of the two-component spinor formalism, which is new in comparison with those used in the literature, the contributions arising from the fermion superpartners, i.e. neutralino-chargino sector to self-energy of Standard Model electroweak gauge bosons are calculated. Corresponding descendants the S, T and U parameters are presented. The validity of our results is examined in two ways, which are then followed by detailed analysis on the results in the literature.

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