- Duffin–Kemmer–Petiau algebra
-
In mathematical physics, the Duffin–Kemmer–Petiau algebra (DKP algebra) is the algebra which is generated the Duffin–Kemmer–Petiau matrices, introduced by Duffin, Kemmer and Petiau.
These matrices have the defining relation[1]
- βμβνβα + βαβνβμ = gμνβα + gαμβν
where gμν is the Galilean metric, represented by the Kronecker symbol gμν = δμν.
The Duffin–Kemmer–Petiau matrices form part of the Duffin–Kemmer–Petiau equation, which describes spin-0 and spin-1 particles in the description of the standard model and is closely linked to the Proca equations[1] and the Klein–Gordon equation.[2] The Duffin–Kemmer–Petiau equation suffers the same drawback as the Klein–Gordon equation in that it calls for negative probabilities.[2]
The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spin‐0 and spin‐1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements.[3]
It has been shown that the equation is closely linked to the De Donder–Weyl covariant Hamiltonian field equations.[4]
Further reading
- Pavel Winternitz et al (eds.): Symmetry in physics: in memory of Robert T. Sharp, CRM Proceedings and Lecture Notes, 2004, ISBN 0-8218-3409-6, section “Bhabha and Duffin–Kemmer–Petiau equations: spin zero and spin one”, p. 50 ff.
- V. Ya. Fainberg, B. M. Pimentel: Duffin–Kemmer–Petiau and Klein–Gordon–Fock Equations for Electromagnetic, Yang–Mills and external Gravitational Field Interactions: proof of equivalence, hep-th/0003283, submitted 30. March 2000
References
- ^ a b Sergey Kruglov: Symmetry and electromagnetic interaction of fields with multi-spin. A Volume in Contemporary Fundamental Physics, ISBN 1-56072-880-9, 2000, p. 26
- ^ a b Anton Z. Capri: Relativistic quantum mechanics and introduction to quantum field theory, World Scientific, 2002, ISBN 981-238-136-8, p. 25
- ^ Ephraim Fischbach, Michael Martin Nieto, C. K. Scott: Duffin‐Kemmer‐Petiau subalgebras: Representations and applications, Journal of Mathematical Physics, vol. 14, no. 12, 1760 (1973), DOI: 10.1063/1.1666249 (abstract)
- ^ Igor V. Kanatchikov: On the Duffin–Kemmer–Petiau formulation of the covariant Hamiltonian dynamics in field theory, hep-th/9911/9911175v1 (submitted 23. November 1999)
This algebra-related article is a stub. You can help Wikipedia by expanding it. This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.
