Ingo Kirsch and Djordje Sijacki 2002 Class. Quantum Grav. 19 3157 doi:10.1088/0264-9381/19/12/305
From Poincaré to affine invariance: how does the Dirac equation generalize?
Ingo Kirsch1,3 and Djordje Sijacki2
Show affiliationsA generalization of the Dirac equation to the case of affine symmetry, with 
replacing 
, is considered. A detailed analysis of a Dirac-type Poincaré-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component fermionic fields, the constraints on the vector-operator generalizing Dirac's γ matrices, as well as the minimal coupling to (metric-)affine gravity are studied. Finally, a symmetry breaking scenario for 
is presented which preserves the Poincaré symmetry.
- PACS
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03.65.Pm Relativistic wave equations
02.20.Qs General properties, structure, and representation of Lie groups
- MSC
-
81T25 Quantum field theory on lattices
- Subjects
- Dates
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Issue 12 (21 June 2002)
Received 4 December 2001
Published 27 May 2002
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From Poincaré to affine invariance: how does the Dirac equation generalize?
Ingo Kirsch and Djordje Sijacki 2002 Class. Quantum Grav. 19 3157
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