| 1. | Fermions are described by spinor field, while bosons by tensor field.
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| 2. | In physics, tensor fields describe bosons and spinor fields describe fermions.
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| 3. | In physics fermions are described by spinor fields and bosons by tensor fields.
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| 4. | For example, local gauge transformations apply to both a vector and spinor field:
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| 5. | The above can be generalized for vector fields, tensor fields, and spinor fields.
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| 6. | They are a special kind of spinor field related to Killing vector fields and Killing tensors.
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| 7. | This is mathematically contained in the spinor fields which are the solutions of the relativistic wave equations.
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| 8. | The solutions to ( ) are multi-component spinor fields, and each component satisfies ( ).
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| 9. | The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields.
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| 10. | Note that in the presence of spinor fields, the Palatini action implies that d \ omega is nonzero.
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