In mathematical physics, the DuffinâKemmerâPetiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the DuffinâKemmerâPetiau matrices. These matrices form part of the DuffinâKemmerâPetiau equation that provides a relativistic description of spin-0 and spin-1 particles.
The DKP algebra is also referred to as the meson algebra. [1]
The DuffinâKemmerâPetiau matrices have the defining relation [2]
where stand for a constant diagonal matrix. The DuffinâKemmerâPetiau matrices for which consists in diagonal elements (+1,-1,...,-1) form part of the DuffinâKemmerâPetiau equation. Five-dimensional DKP matrices can be represented as: [3] [4]
These five-dimensional DKP matrices represent spin-0 particles. The DKP matrices for spin-1 particles are 10-dimensional. [3] The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spinâ0 and spinâ1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements. [5]
The DuffinâKemmerâPetiau equation (DKP equation, also: Kemmer equation) is a relativistic wave equation which describes spin-0 and spin-1 particles in the description of the standard model. For particles with nonzero mass, the DKP equation is [2]
where are DuffinâKemmerâPetiau matrices, is the particle's mass, its wavefunction, the reduced Planck constant, the speed of light. For massless particles, the term is replaced by a singular matrix that obeys the relations and .
The DKP equation for spin-0 is closely linked to the KleinâGordon equation [4] [6] and the equation for spin-1 to the Proca equations. [7] It suffers the same drawback as the KleinâGordon equation in that it calls for negative probabilities. [4] Also the De DonderâWeyl covariant Hamiltonian field equations can be formulated in terms of DKP matrices. [8]
The DuffinâKemmerâPetiau algebra was introduced in the 1930s by R.J. Duffin, [9] N. Kemmer [10] and G. Petiau. [11]
In mathematical physics, the DuffinâKemmerâPetiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the DuffinâKemmerâPetiau matrices. These matrices form part of the DuffinâKemmerâPetiau equation that provides a relativistic description of spin-0 and spin-1 particles.
The DKP algebra is also referred to as the meson algebra. [1]
The DuffinâKemmerâPetiau matrices have the defining relation [2]
where stand for a constant diagonal matrix. The DuffinâKemmerâPetiau matrices for which consists in diagonal elements (+1,-1,...,-1) form part of the DuffinâKemmerâPetiau equation. Five-dimensional DKP matrices can be represented as: [3] [4]
These five-dimensional DKP matrices represent spin-0 particles. The DKP matrices for spin-1 particles are 10-dimensional. [3] The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spinâ0 and spinâ1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements. [5]
The DuffinâKemmerâPetiau equation (DKP equation, also: Kemmer equation) is a relativistic wave equation which describes spin-0 and spin-1 particles in the description of the standard model. For particles with nonzero mass, the DKP equation is [2]
where are DuffinâKemmerâPetiau matrices, is the particle's mass, its wavefunction, the reduced Planck constant, the speed of light. For massless particles, the term is replaced by a singular matrix that obeys the relations and .
The DKP equation for spin-0 is closely linked to the KleinâGordon equation [4] [6] and the equation for spin-1 to the Proca equations. [7] It suffers the same drawback as the KleinâGordon equation in that it calls for negative probabilities. [4] Also the De DonderâWeyl covariant Hamiltonian field equations can be formulated in terms of DKP matrices. [8]
The DuffinâKemmerâPetiau algebra was introduced in the 1930s by R.J. Duffin, [9] N. Kemmer [10] and G. Petiau. [11]