Duffin Kemmer Petiau Research Articles

The group structure of pseudo-Riemannian curvature spaces

The linear conformal group G (pseudo-orthogonal automorphisms and dilatations) on a pseudo-orthogonal vector space induces an action in the space of pseudo-orthogonal curvature structures, which leaves Singer and Thorpe’s direct decomposition in trivial, non-Einsteinian and Weyl curvature structures invariant. It is shown that the condition of a curvature to be homogeneous, reductive, or symmetric is G-invariant. A condition for a non-Weyl curvature to be symmetric is formulated explicitly. Nomizu’s injection of the Jordan algebra of Lorentz-self-adjoint matrices is used to describe some G-orbits of non-Einsteinian curvatures. The Duffin–Kemmer–Petiau meson triple allows the construction of a cosmological model with trivial curvature.

Historical development of the Bhabha first-order relativistic wave equations for arbitrary spin

From letters, personal reminiscences, and the published works of the authors involved, we describe the historical development of the Bhabha system of first-order relativistic wave equations for arbitrary spin. The simplest special cases of these equations reduce to the Dirac and DKP (Duffin–Kemmer–Petiau) equations for spin-1/2 and spins 0 and 1, respectively.

Noncausal propagation in spin-0 theories with external field interactions

The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. The results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2(2J + 1)-component Schroedinger form

Bhabha first-order wave equations. II. Mass and spin composition, Hamiltonians, and general Sakata-Taketani reductions

Beginning with the Bhabha first-order wave equation of maximum spin 1 [the Duffin-Kemmer-Petiau (DKP) equation], where Sakata and Taketani (ST) separated out the "particle components" from the built in "subsidiary components," we derive for the first time the Hamiltonian equation for the "subsidiary components," and show that its solution is an identity in terms of the particle-components solution. We then derive a set of general inverse and ST operators for arbitrary-spin Bhabha fields. With these generalized operators we can discuss and understand the mass and spin composition of a general Bhabha so(5) field, it being a particular sum of [$2\ifmmode\times\else\texttimes\fi{}(2S+1)$] components for each particular mass and spin ($S$) state, as well as built in "subsidiary components" for integer spin. We then can use these general inverse and ST operators to (a) derive the general Bhabha Hamiltonian for arbitrary spin, (b) decouple the "particle components" from the "subsidiary components" in the Hamiltonian equations for integer spin (where, as was the case for DKP, we find that the Hamiltonian "subsidiary components" solution is an identity in terms of the particle-components solution), and (c) decouple the $\mathcal{S}+\frac{1}{2} (\mathcal{S})$ different mass states for half-integer (integer) spin. We discuss the physical implications of this observation and other aspects of our results.

Bhabha first-order wave equations: I.C,P, andT

We discuss properties of Bhabha first-order wave equations for arbitrary spin, of which the Dirac and Duffin-Kemmer-Petiau (DKP) equations are special examples. The $C$, $P$, and $T$ transformation matrices for the Dirac field are reviewed in various representations, and the $C$, $P$, and $T$ transformation matrices for the DKP and general Bhabha cases are then derived. The Bhabha transformation matrices are polynomials of order $2\mathcal{S}$ in the algebra matrices, where $\mathcal{S}$ is the maximum spin of a particular Bhabha algebra. For the cases $\mathcal{S}=1 \mathrm{and} \frac{1}{2}$ they reduce to the DKP and Dirac transformation matrices. We also discuss $C$, $P$, and $T$ for the Sakata-Taketani (ST) reduction of the DKP equation, and explicitly exhibit the subsidiary component ST Hamiltonian equation, as well as the known particle component ST equation. Throughout we emphasize that physical insight which can be gained from the use of the first-order Bhabha formalism, including a possible connection between meson nonconservation and $\mathrm{CP}$ violation.

Meson decays and the DKP equation

It has been argued that the Duffin-Kemmer-Petiau (DKP) description of mesons fails in predicting meson decay rates and the strong-interaction $\frac{D}{F}$ ratio, while the Klein-Gordon (KG) description succeeds. It is shown here that these arguments are deficient in three respects: (a) The various dynamical assumptions used in comparing the DKP and the KG descriptions preclude a rigorous test of their relative merits at present, except in some particularly simple cases; (b) if the same phenomenological freedom were used in the two descriptions the results could be made similar; and (c) actually, when worked out systematically on the basis of a Lagrangian formalism, it is the DKP rather than the KG description which can extract a consistent strong-interaction $\frac{D}{F}$ ratio.

The Lie algebra s o (N) and the Duffin-Kemmer-Petiau ring

An explicit expression is given for the unit element E of the ring generated by the Duffin-Kemmer-Petiau (DKP) operators βμ. The relation of E to the unit operator I (unit matrix in a matrix representation) is also derived. It is pointed out that one must be careful to distinguish E from I. Bhabha's observation that one may use the irreducible representations (irreps) of the Lie algebra s o (5) to obtain the irreps of the Dirac, DKP, and other algebras is given a concise and general setting in terms of a relation between the Lie algebra s o (n + 1) and a family of semisimple operator rings. We emphasize that for the case n + 1 = 5 this means that there is an underlying relationship between the physical DKP and Dirac algebras and wave equations.

SU(3)-Symmetric Coupling of Mesons to Baryons and the StrongDFRatio

Pseudoscalar meson-baryon-baryon ($\mathrm{PBB}$) couplings are analyzed in both the Klein-Gordon (KG) and Duffin-Kemmer-Petiau (DKP) formalisms. Present determinations of these coupling constants indicate that both the pseudoscalar (ps) and pseudovector (pv) KG couplings are in relatively poor agreement with SU(3), whereas the pv DKP coupling is in excellent agreement with SU(3). Furthermore, the value $\ensuremath{\beta}=\frac{D}{(D+F)}=0.71\ifmmode\pm\else\textpm\fi{}0.07$ extracted from the DKP coupling is close to the canonical SU(6) value $\ensuremath{\beta}=0.6$.

Spin-0 Phenomenology ofKl3Decays in theK*-Pole Model

We present a detailed discussion of both the Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) ${K}^{*}$-pole model descriptions of ${K}_{l3}$ decays, and compare them to experiment. Significant differences are found between the two models, with the experimental data tending to favor the DKP version. In three Appendixes we explain in detail important aspects of using the DKP formulation to describe ${K}_{l3}$ decays.