Constraints on composite Dirac neutrinos from observations of galaxy clusters

Recently, to explain the origin of neutrino masses a model based on confining some hidden fermionic bound states into right-handed chiral neutrinos has been proposed. One of the consequences of condensing the hidden sector fields in this model is the presence of sterile composite Dirac neutrinos of keV mass, which can form viable warm dark matter particles. We have analyzed constraints on this model from the observations of satellite based telescopes to detect the sterile neutrinos in clusters of galaxies.     

Incomplete Dirac reduction of constrained Hamiltonian systems

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.     

Cosmological imprints of Dirac neutrinos in a keV-vacuum 2HDM

The Dirac neutrino masses could be simply generated by a neutrinophilic scalar doublet with a vacuum being dramatically different from the electroweak one. While the case with an eV-scale vacuum has been widely explored previously, we exploit in this work the desert where the scalar vacuum is of begin{document}$mathcal{O}(mathrm{keV})$end{document} scale. In this regime, there would be rare hope to probe the keV-vacuum neutrinophilic scalar model via the lepton-flavor-violating processes, which makes it distinguishable from the widely considered eV-scale vacuum. Although such a keV-vacuum scenario is inert in the low-energy flavor physics, we show that the baryogenesis realized via the lightest Dirac neutrino can be a natural candidate in explaining the baryon asymmetry of the Universe. Furthermore, the Dirac neutrinos with a keV-vacuum scalar can generate a shift of the effective neutrino number within the range begin{document}$0.097leqslant Delta N_{rm eff}leqslant 0.112$end{document}, which can be probed by the future Simons Observatory experiments. In particular, the model with a minimal value begin{document}$Delta N_{rm eff}=0.097$end{document} can already be falsified by the future CMB Stage-IV and Large Scale Structure surveys, providing consequently striking exploratory avenues in the cosmological regime for such a keV-vacuum scenario.     

Dirac Equation from the Hamiltonian and the Case With a Gravitational Field

Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation—in special coordinates. To use the equation in the static-gravitational case, we need to rewrite it in more general coordinates. This can be done only if the usual, spinor transformation of the wave function is replaced by the 4-vector transformation. We show that the latter also makes the flat-spacetime Dirac equation Lorentz-covariant, although the Dirac matrices are not invariant. Because the equation itself is left unchanged in the flat case, the 4-vector transformation does not alter the main physical consequences of that equation in that case. However, the equation derived in the static-gravitational case is not equivalent to the standard (Fock-Weyl) gravitational extension of the Dirac equation.     

The Dirac Equation in the Bertotti-Robinson Space-Time

The Dirac equation is considered in the uniform electromagnetic field space of Bertotti-Robinson with charge coupling. The methods of separation of variables and decoupling are easily achieved. The separated axial equation is reduced to a rare Riccati type of differential equation. The behaviour of potentials, their asymptotic solutions and the conserved currents of the Dirac equation are found.     

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time

This is the second of a couple of papers in which we aim to show the peculiar capability of the Hamiltonian ADM formulation of metric gravity to grasp a series of conceptual and technical problems that appear to have not been directly discussed so far. In this paper we also propose new viewpoints about issues that, being deeply rooted into the foundational level of Einstein theory, seem particularly worth of clarification in connection with the alternative programs of string theory and loop quantum gravity. The achievements of the present work include: (1) the analysis of the so-called Hole phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of spatially non-compact Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the weak ADM energy. It is crucial to our analysis the re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081); (2) the utilization of the Bergmann-Komar intrinsic pseudo-coordinates, defined as suitable functionals of the Weyl curvature scalars, as tools for a specific gauge-fixing to the super-hamiltonian and super-momentum constraints; (3) the consequent construction of a physical atlas of 4-coordinate systems for the 4-dimensional mathematical manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent Dirac observables). Such construction embodies the physical individuation of the points of space-time as point-events, both in absence and presence of matter, and associates a non-commutative structure to each gauge fixing or 4-dimensional coordinate system; (4) a clarification of the multiple definition given by Peter Bergmann of the concept of (Bergmann) observable in general relativity. This clarification leads to the proposal of a main conjecture asserting the existence of: i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) change in the observable quantities of general relativity; (5) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a standard of space-time more or less like atomic clocks define standards of time. In the end, against the well-known Einstein's assertion according to which general covariance takes away from space and time the last remnant of physical objectivity, we conclude that point-events maintain a peculiar sort of objectivity. Also, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of participating directly in the individuation process, being involved in the determination of the Dirac observables. Finally, some hints following from our approach for the quantum gravity programme are suggested.     

Treatment of Dirac Fields in Light—Front Coordinates by Dirac‘s Method for Constrained Hamiltonian Systems

Dirac‘s method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.     

非对易相空间中的狄拉克振子的能级和Wigner函数

非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并利用非对易相空间量子力学的代数关系,讨论了非对易相空间中狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数.     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.     

The spacetime of a Dirac fermion

We present an approximate solution to the minimally coupled Einstein-Dirac equations. We interpret the solution as describing a massive fermion coexisting with its own gravitational field. The solution is axisymmetric but is time dependent. The metric approaches that of a flat spacetime at the spatial infinity. We have calculated a variety of conserved quantities in the system.     

The CPT Group of the Dirac Field

Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields , and , where and . These sets are given by , , and , , . Then , and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively, and , which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that and , where is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of by , isomorphic to a semidirect product of these groups; S₆ and S₈ are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group , which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with , which is then called the matrix CPT group. It turns out that , where is the dicyclic group of 8 elements and S₁₀ is the symmetric group of 10 elements. Since , the quaternion group, and , the 0-sphere, then .     

The Dirac spectrum of Bieberbach manifolds

The Dirac spectra and the eta invariants of three-dimensional Bieberbach manifolds are computed. Compact connected three-dimensional spin manifolds admitting parallel non-vanishing spinors are identified as flat tori.     

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics ofa particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

The Three-Dimensional Dirac Oscillator in the Presence of Aharonov-Bohm and Magnetic Monopole Potentials

No Heading We study the Dirac equation in 3+1 dimensions with non-minimal coupling to an isotropic radial three-vector potential and in the presence of a static electromagnetic potential. The space component of the electromagnetic potential has angular (non-central) dependence such that the Dirac equation separates completely in spherical coordinates. We obtain solutions for the case where the three-vector potential is linear in the radial coordinate (Dirac oscillator) and the time component of the electro-magnetic potential vanishes. The relativistic energy spectrum and spinor eigenfunctions are obtained.     

Quantum Aspects of the Fundamental Dirac Membrane Model

The classical relativistic Hamiltonian derived by Dirac for a charged membrane is written in a linearized form and it is pointed out that the membrane has spin 1/2 under the action of an external magnetic field. A spin-rotation coupling term is included into the linearized Hamiltonian and the corresponding wave equation for the membrane is written. It leads to quantized radial modes of oscillations and its first eigenvalues are derived numerically. Asymptotic solutions are also considered.