Massless Field Equations Research Articles

Massless field equations for spin 3/2 in dimension 6

Main topic of the paper is a study of properties of massless fields of spin 3/2. A lot of information is available already for massless fields in dimension 4. Here, we concentrate on dimension 6 and we are using the fact that the group SL(4,C) is isomorphic with the group Spin(6,C). It makes it possible to use tensor formalism for massless fields. Main problems treated in the paper are a description of fields which need to be considered in the spin 3/2 case, a suitable choice of equations they should satisfy, irreducibility of homogeneous solutions of massless field equations, the Fischer decomposition and the Howe duality for such fields.

Scattering on self-dual Taub-NUT

We derive exact solutions of massless free field equations and tree-level two-point amplitudes up to spin 2 on self-dual Taub-NUT (SDTN) spacetime, as well as on its single copy, the self-dual dyon (SDD). We use Killing spinors to build analogues of momentum eigenstates, finding that, in the spirit of color-kinematics duality, those for the SDD lift directly to provide states on the SDTN background if one replaces charge with energy. We discover that they are forced to have faster growth at infinity than in flat space due to the topological non-triviality of these backgrounds. The amplitudes for massless scalars and spinning particles in the and helicity configurations vanish for generic kinematics as a consequence of the integrability of the self-dual sector. The amplitudes are non-vanishing and we compute them exactly in the backgrounds, which are treated non-perturbatively. It is explained how spin is easily introduced via a Newman–Janis imaginary shift along the spin-vector leading directly to the well-known exponential factor in the dot product of the spin with the momenta. We also observe a double copy relation between the gluon amplitude on a SDD and graviton amplitude on a SDTN spacetime.

Soliton-like solutions of nonlinear scalar and electromagnetic field equations in gravitational theory

In this work, exact analytical static spherical symmetric solutions to the nonlinear interacting electromagnetic and massless scalar field equations have been determined taking into account the proper gravitational field of elementary particles. The obtained results prove that all solutions of the Einstein equation and those of the interacting fields are regular with localized energy density. All non-zero components of the 4-vector potential are solutions to the inverted Painlevé-Gambier XI equation. Moreover, the total energy of interacting fields is limited and the total charge of elementary particles is finite. These solutions obtained are soliton-like and can be used as a model to describe the internal structure of elementary particles.

Unification of massless field equations solutions for any spin

A unification in terms of exact solutions for massless Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre-potential functions, which satisfy the d'Alembert equation. The coupled equations satisfied by the pre-potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre-potentials that satisfy the usual wave equation which may be used to construct exact non-trivial solutions to Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to a unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre-potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Fischer Decomposition of Massless Fields for Spin 3/2 in Dimension 4

As an analogue of the massless field equations in Euclidean space, we consider the so-called generalized Cauchy–Riemann equations introduced by E. Stein and G. Weiss. In the spin 1/2 case these equations reduce to the Dirac equation for spin 1/2 fields, which was thoroughly and intensively studied in Clifford analysis. For general spin it was recently shown that, in dimension 4, homogenous solutions form irreducible Spin modules. The next step then is to describe the corresponding Fischer decomposition, i.e. an irreducible decomposition of the space of spinor fields, which is well-known for spin 1/2 and for spin 1. The main aim of the present paper is to describe, still in dimension 4, the Fischer decomposition for spin 3/2.

The σ− Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ− cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in AdS4. In the d-dimensional case Hp(σ−) is computed for any p and interpretation of Hp(σ−) is given both for the original Fronsdal system and for the associated systems of higher form fields.

General massless field equations for higher spin in dimension 4

Massless field equations are fundamental in particle physics. In Clifford analysis, the Euclidean version of these equations has been dealt with, but it is not clear, even in dimension 4, what should be the right analogue of massless field equations for fields with values in a general irreducible Spin(4)‐module. The main aim of the paper is to explain that a good possibility is to take the so‐called generalized Cauchy–Riemann equations proposed a long time ago by Stein and Weiss. For this choice of the equations, we show that their polynomial solutions form different irreducible Spin(4)‐modules. This is an important step in developing the corresponding function theory.

Hawking radiation by spherically-symmetric static black holes for all spins: Teukolsky equations and potentials

In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherically-symmetric and static metrics. We then compute the short-ranged potentials associated with the radial dynamics of spin 1 and spin 1/2 fields, thereby completing the existing literature on spin 0 and 2. These potentials are crucial for the computation of Hawking radiation and quasi-normal modes emitted by black holes. In addition to the Schwarzschild metric, we apply these results and give the explicit formulas for the radial potentials in the case of charged (Reissner--Nordstr\"om) black holes, higher-dimensional black holes, and polymerized black holes arising from loop quantum gravity. These results are in particular relevant and applicable to a large class of regular black hole metrics. The phenomenological applications of these formulas will be the subject of a companion paper.

Massless field equations in comoving spherically symmetric metric and solution in LTB cosmology

Massless field equations in comoving spherically symmetric metric and solution in LTB cosmology

De Sitter field equations from quadratic curvature gravity: A group theoretical approach

In this paper, the linearized field equations related to the quadratic curvature gravity theory have been obtained in the four-dimensional de Sitter (dS) space–time. The massless spin-2 field equations have been written in terms of the Casimir operators of dS group making use of the ambient space notations. By imposing some simple constraints, arisen from group theoretical interpretation of the field equations, a new four-dimensional Gauss–Bonnet (GB-)like action has been introduced with the related field equations transforming according to the unitary irreducible representations (UIRs) of dS group. Since, the field equations transform according to the UIRs of dS group, the GB-like action, we just obtained, is expected to be a successful model of modified gravity. For more clarity, the gauge invariant field equations have been solved in terms of a gauge-fixing parameter [Formula: see text]. It has been shown that the solution can be written as the multiplication of a symmetric rank-2 polarization tensor and a massless minimally coupled scalar field on dS space. The Krein–Gupta–Bleuler quantization method has been utilized and the covariant two-point function has been calculated in terms of the massless minimally coupled scalar two-point function, using the ambient space notations. It has been written in terms of dS intrinsic coordinates from the ambient space counterpart. The two-point functions are dS invariant and free of any theoretical problems. It means that the proposed model is a successful model of modified gravity and it can produce significant results in the contexts of classical theory of gravity and quantum gravity toy models.

Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime

We examine the solutions of the semilinear wave equation, and, in particular, of the [Formula: see text] model of quantum field theory in the curved spacetime. More exactly, for [Formula: see text] we prove that the solution of the massless self-interacting scalar field equation in the Einstein–de Sitter universe has finite lifespan.

Hybrid imploding scalar and ads spacetime

A solution to the massless scalar cosmological constant field equations is presented. The solution has imploding scalar and parts of anti-deSitter or deSitter spacetime as limiting cases. Some of the solutions properties are discussed however not much can be said because of the contrasting properties of imploding scalar and deSitter spacetimes. What can be said is that the self-similar homeothetic Killing vector is not qualitatively changed by the cosmological constant, in other words self-similarity and the presence of a cosmological constant are separate properties.

Acoustic analog of gravitational wave

We explore nonlinear perturbations in different static fluid systems. We find that the equations, corresponding to the perturbation of the integrals of motion, i.e; Bernoulli's constant and the mass flow rate, satisfy massless scalar field equation in a time dependent acoustic metric. When one is interested up to the second order behaviour of the perturbations, the emergent time dependent acoustic metric of the system, derived from the massless scalar field equations of the perturbations of the integrals of motion, has some astounding similarities with the metric describing gravitational wave in Minkowski spacetime.

Spin raising and lowering operators for Rarita-Schwinger fields

Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-$\frac{3}{2}$ massless Rarita-Schwinger equation from source-free Maxwell fields and twistor spinors are constructed. It is shown that this construction requires Ricci-flat backgrounds due to the gauge invariance of the massless Rarita-Schwinger equation. Constraints to construct spin raising and lowering operators for Rarita-Schwinger fields are found. Symmetry operators for Rarita-Schwinger fields via twistor spinors are obtained.

Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4

The massless field equations for lower integer and half-integer values of spin in Minkowski space are fundamental equations in mathematical physics. Their counterpart in Euclidean spacetime is a system of elliptic equations, which was already studied from the viewpoint of function theory in the framework of so-called Hodge systems for differential forms of various degrees. In dimension 4 it is possible to substitute spinor calculus for the usual tensor notation. In the present paper we concentrate on the case of the massless field equation for spin 1 in dimension 4, and we treat, in a spinor formalism, a fundamental concept of its function theory: the Fischer decomposition of polynomial spinor fields, for which we give simple and independent proofs.

Analysis of the wave equations for the near horizon static isotropic metric

We find that, for the near horizon static isotropic metric, all of the massless field equations of the spin $\ensuremath{\le}2$ have the same characteristic: they can be reduced to the Fuchsian-type equation with three regular singular points. Three general solutions, corresponding to different parameter values, are obtained. Two of the solutions have discrete imaginary frequencies. Based on the results above, we obtain exact formulas for the quasinormal modes of the Rindler-type spacetime. We also derive an elegant wave equation, which is the fundamental formula of the perturbation theory for general static spherically symmetric spacetime.

Spinor description of the curvatures of D = 5 gauge fields

Spinor description of the curvatures of D = 5 Yang–Mills, Rarita–Schwinger and gravitational fields is considered. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are studied. In the absence of sources symmetric curvature spinors with 2s indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to 4d case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold SO(1, 4)/(SO(1,1) × ISO(3)) isomorphic to the three-sphere is considered.

Spinor description of D = 5 massless low-spin gauge fields

Spinor description for the curvatures of D = 5 Yang–Mills, Rarita–Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere is proposed. The states in its spectrum are given by the functions on S3 that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various supermultiplets of D = 5 space–time supersymmetry.

Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

In the present paper we discuss the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields based on sedeonic space-time operators and sedeonic wave functions.

A unified model with a generalized gauge symmetry and its cosmological implications

A unified model is based on a generalized gauge symmetry with groups [SU3c]color×(SU2×U1)× [U1b×U1l]. It implies that all interactions should preserve conservation laws of baryon number, lepton number, and electric charge, etc. The baryonic U1b, leptonic U1l and color SU3c gauge transformations are generalized to involve nonintegrable phase factors. One has gauge invariant fourth-order equations for massless gauge fields, which leads to linear potentials in the [U1b×U1l] and color [SU3c] sectors. We discuss possible cosmological implications of the new baryonic gauge field. It can produce a very small constant repulsive force between two baryon galaxies (or between two anti-baryon galaxies), where the baryon force can overcome the gravitational force at very large distances and leads to an accelerated cosmic expansion. Based on conservation laws in the unified model, we discuss a simple rotating dumbbell universe with equal amounts of matter and anti-matter, which may be pictured as two gigantic rotating clusters of galaxies. Within the gigantic baryonic cluster, a galaxy will have an approximately linearly accelerated expansion due to the effective force of constant density of all baryonic matter. The same expansion happens in the gigantic anti-baryonic cluster. Physical implications of the generalized gauge symmetry on charmonium confining potentials due to new SU3c field equations, frequency shift of distant supernovae Ia and their experimental tests are discussed.