Valeri V. Dvoeglazov

Neutral particles in light of the Majorana-Ahluwalia ideas

The first part of this article presents an overview of the theory and phenomenology of truly neutral particles based on the papers of Majorana, Racah, Furry, McLennan, and Case. The recent development of the construct undertaken by Ahluwalia could be relevant for the explanation of the present experimental situation in neutrino physics and astrophysics. Then the new fundamental wave equations for self-/anti-self-conjugate type II spinors proposed by Ahluwalia are recast into covariant form. The connection with Foldy-Nigam-Bargmann-Wightman-Wigner (FNBWW)-type quantum field theory is found. Possible applications to the problem of neutrino oscillations are discussed.

Normalization and the m → 0 limit of the Proca theory

We repeat the known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. The importance of the normalization is point out for the problem of the correct description of spin-1 quantized fields. Finally, the discussion of the so-called Kalb-Ramond field is presented.We repeat the known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. The importance of the normalization is pointed out for the problem of the correct description of spin-1 quantized fields. Finally, the discussion of the so-called Kalb-Ramond field is presented.

Quantized (1, 0) % (0, 1) Fields

We find a mapping between antisymmetric tensormatter fields and the Weinberg 2(2j + 1)-component“bispinor” fields. Equations which describethe j = 1 antisymmetric tensor field coincide with the Hammer-Tucker equations entirely and withthe Weinberg ones within a subsidiary condition, theKlein-Gordon equation. A new Lagrangian for the Weinbergtheory is proposed which is scalar and Hermitian. It is built on the basis of the concept of“Weinberg doubles.” The origin of acontradiction between the classical theory, the Weinbergtheorem B – A = λ for quantum relativisticfields, and the claimed ‘longitudity’ of the antisymmetrictensor field [transformed on the (1, 0) ⊕ (0, 1)Lorentz group representation] after quantization isclarified. Analogs of the j = 1/2 Feynman–Dysonpropagator are presented in the framework of the j = 1 Weinberg theory.It is then shown that under a definite choice of fieldfunctions and initial and boundary conditions themassless j = 1 Weinberg–Tucker–Hammerequations contain all the information that the Maxwell equationsfor the electromagnetic field have. Thus, the formerappear to be of use in describing some physicalprocesses.

Lagrangian for the Majorana-Ahluwalia construct

SummaryEquations describing self/anti-self-charge conjugate states, recently proposed by Ahluwalia, are re-written in covariant form. The corresponding Lagrangian for the neutral-particle theory is proposed. From a group-theoretical viewpoint the construct is an example of the Nigam-Foldy-Bargmann-Wightman-Wigner-type quantum field theory based on the doubled representations of the extended Lorentz group. Relations with the Sachs-Schwebel and Ziino-Barut concepts of relativistic quantum theory are discussed.

Extra Dirac equations

SummarySurprising symmetries in the (j, 0) ⊕ (0,j) Lorentz-group representation space are analysed. The aim is to draw the reader’s attention to the possibility of describing the particle world on the grounds of the Dirac «doubles». Several tune points of the variational principle for this kind of equations are briefly discussed.

The Barut Second-Order Equation, Dynamical Invariants and Interactions

The second-order equation in the (1/2, 0) ⊕ (0, 1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s, ref. [1]. It permits to explain the mass splitting of leptons (e, μ, τ). Recently, the interest has grown to this model (see, for instance, the papers by S. Kruglov [2] and J. P. Vigier et al. [3]). We continue the research deriving the equation from the first principles, finding the dynamical invariants for this model, investigating the influence of the potential interactions. The Barut main equation is

Helicity basis and parity

We study the theory of the (1/2,0) ⊕ (0,1/2) representation in helicity basis. Helicity eigenstates are not the parity eigenstates. This is in accordance with the consideration of Berestetskii, Lifshitz, and Pitaevskii. Relations to the Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new form of the parity operator is proposed. It commutes with the Hamiltonian.

A note on the relativistic covariance of the B-cyclic relations

It is shown that the Evans-Vigier modified electrodynamics is compatible with relativity theory.

The Bargmann-Wigner formalism for spin 2 fields

The Bargmann-Wigner formalism has been applied to describe the spin-2 field in terms of the symmetric fourth-rank multi-Dirac spinor Ψαβγδ. A serious problem of the standard anzatz is that the resulting equation of motion has the trivial solution with all field components being independently equal to zero. We here show that this problem is an artefact of the neglection of terms containing the matrix γ5 in the decomposition of ϕ into the Clifford algebra basis. We further emphasize importance of the gauge 4-vector field in that respect.

Different Quantum Field Constructions in the (1/2,0) ⊕ (0,1/2) Representation

We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)⊕ (0,1/2) field and developing the Majorana–McLennan–Case–Ahluwalia construction for neutrino, we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.