The Bargmann-Wigner formalism for spin 2 fields

Abstract

Abstract. The Bargmann-Wigner formalism has been applied to describe the spin-2 field in terms of the symmetric fourth-rank multi-Dirac spinor ~~~~~. 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 "/~ in the decomposition of 9 into the Clifford algebra basis. We further emphasize importance o[ the gauge 4-vector field in that respect.

Chiral Bargmann-Wigner Equations for Spin-1 Massive Fields

“…A field of rest mass m and spin s ≤ 1/2 is described by a symmetric multispinor for which the Bargmann-Wigner (BW) equations are derived [1]. For special cases of s = 1/2, s = 1 and s = 3/2, the BW equations reduce to the Dirac [4], Proca [5] and Rarita-Schwinger [6] equations, respectively; however, for s = 2, see [7]. The BW equations are coupled first-order partial differential equation with the original Dirac operator ( D = iγ µ ∂ µ −m) acting on multispinor wavefunctions.…”

Fully Symmetric Relativistic Quantum Mechanics and Its Physical Implications

“…There were several attempts to generalize the RQM equations, specifically, the Klein-Gordon [16][17][18][19], Dirac [20][21][22][23][24][25], or both Klein-Gordon and Dirac [26][27][28] and other [29] equations. Physical motivations for these generalizations were different and they range from including some supersymmetry effects to unification of leptons and quarks and accounting for different masses of the three generations of elementary particles.…”

Non-smooth Gravity and Parity Violation

“…where the superscript notation is just to remind us the position of the indices of the Riemann tensor that are being contracted, e.g. R (12) ρσ is the result of contracting the first and second indices of the Riemann tensor. All the other contractions of the Riemann tensor are either zero or proportional to the above ones.…”

“…(2) that the majority of the Riemann tensor symmetries are broken with the exception of the skew-symmetry of the last two indices R µνρσ = −R µνσρ . This implies the existence of different "Ricci tensors": R (12) ρσ ≡ g µν R µνρσ ,…”

“…In general relativity, the only curvature invariant that contains up to two derivatives of the metric is the Ricci scalar R. However, in the present paper, due to the broken symmetries of the Riemann tensor, another invariant is present. To show this, let us define the dual curvature by [12]…”