Sign Convention Linkage: Metric Tensor & Dirac Equation

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The discussion centers on the relationship between the sign convention of the metric tensor and the Dirac equation, questioning whether a (-,+,+,+) convention can coexist with a metric of the form dt^2 - dX^2 - dY^2 - dZ^2. Participants note that the Dirac algebra appears to be influenced by the metric's sign convention. There is a request for a step-by-step derivation of the Dirac equation using an alternative sign convention, indicating a desire for clarity on this mathematical relationship. Some contributors express confusion regarding differing definitions of the Hamiltonian in relation to the metric. The conversation highlights the complexities of aligning these fundamental concepts in theoretical physics.
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Does anyone know if the sign convenmtion from the metric tensor is linked to the sign convention in the Dirac equation. i.e is it possible to have a dt^2 - dX^2-dY^2-dZ^2 metric,

with a (-,+,+,+) convention for the Dirac equation?
 
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unfortunately i agree but i have been working through. http://arxiv.org/abs/hep-ph/0003045v3 and they seem to define the hamiltonian in a different way to the metric.
 
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sorry what do you mean?
 

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