Duffin–Kemmer–Petiau Particles are Bosons

Abstract

The parametrized Duffin-Kemmer-Petiau wave equation is formulated here for many relativistic particles of spin-0 or spin-1. The conventional second-quantized or Fock-space proof of the spin-statistics connection requires that the fields of creation and annihilation operators satisfy commutation relations subject to causality conditions. The conditions restrict entanglement to spacelike separations of the order of the Compton wavelength /mc. Relativistic quantum mechanics is used here to prove the symmetry of the wavefunctions for identical particles, following the nonrelativistic argument of Jabs (Found. Phys. 2010, 40, 776-792). First quantization does not require causal commutation relations, and so entanglement is unrestricted.

Feynman-Stueckelberg electroweak interactions and isospin entanglement

“…3. Absent the causal commutator and causal anticommutator relations of QFT, the spin statistics connection is established using Jab's rule [20,21] extended to the relativistic regime [3]. When exchanging wavefunctions for two identical particles, the exchange of the angles of phase relative to the axis of spin must be homotopically consistent.…”

“…where µ and λ are positive constants. The parameter τ is active in the Lagrange density (3) as a fourth spacelike dimension, but again the metric g µν is restricted to R 4 and Lorentz covariance is similarly restricted to spacetime. The τ -integral of the potential (7) has local extrema.…”

“…It is occasionally clearer to express p dependence as an argument rather than a subscript, thus for example ̟(p) ≡ ̟ p . Details of the free wavefunctions, discrete symmetries and influence functions may be found in [1], although the sign conventions here follow [3]. The normalizations factor here for the spinor amplitudes of a free electron wavefunction is (E p + m p )/2g e m p where E p = |p 0 | .…”

“…First quantized electrodynamics can be formulated [1] in terms of an unbounded real variable τ , the so-called Stueckelberg-Feynman parameter [2]. The motivation for the first quantized formulation is that it supports relativistic entanglement without restriction upon the spacetime separation [1,3]. Quantum Field Theory, on the other hand, restricts entanglement to separations of the order of the Compton wavelength [4][5][6][7][8], owing to the field operators being subject to causal commutation and anticommutation relations.…”

“…The findings are summarized in Section IV. Included in A are outlines of the first quantized formulations of pair annihilation and creation, higher order corrections to interactions [1], and the relativistic first quantized establishment [3] of the spin statistics connection.…”