|
| related topics |
| {field, particle, equation} |
| {operator, operators, space} |
| {energy, gaussian, time} |
| {group, space, representation} |
| {observables, space, algebra} |
| {bell, inequality, local} |
| {let, theorem, proof} |
|
Common Space of Spin and Spacetime
Wei Min Jin
abstract: Given Lorentz invariance in Minkowski spacetime, we investigate a common
space of spin and spacetime. To obtain a finite spinor representation of the
non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an
indefinite inner product space (IIPS) with a normalized positive probability.
In this IIPS, the common momentum and common variable of a massive fermion turn
out to be ``doubly strict plus-operators''. Due to this nice property, it is
straightforward to show an uncertainty relation between fermion mass and proper
time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,
and the fermion field equations are derivable from the Lagrangians. Finally,
the nonlinear QED equations and Lagrangians are presented as an example.
- oai_identifier:
- oai:arXiv.org:quant-ph/0409011
- categories:
- quant-ph gr-qc hep-th
- comments:
- 17 pages, a reference corrected, final version published on
Foundations of Physics Letters in June of 2005, as a personal tribute to
Einstein and Dirac
- doi:
- 10.1007/s10702-005-6115-z
- arxiv_id:
- quant-ph/0409011
- journal_ref:
- Found.Phys.Lett. 18 (2005) 243-258
- created:
- 2004-09-01
- updated:
- 2006-08-17
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