Is it possible to use "+/-" as indices?&How to define a commutator?

Question

1.How to make following equation have sense?

{+,-}::Symbol.
ex:=f_{-}+f_{+};

2.How to make all commutators

[a b... , c d...] or \commutaor{a b... }{ c d...]

become

a b... c d... - c d... a b...

Answer 1

Use fm and fp and define

fm{#}::LaTeXForm("{f_{-}}").
fp{#}::LaTeXForm("{f_{+}}").

To expand, use

substitute(_, $\commutator{A??}{B??} -> A?? B?? - B?? A??$);

Does that help?

Comments

Yes, it does. I'm so sorry that I have not give more details about problems. In fact, I want make following equation have sense:

ex:=f_{-\mu\nu}+f_{+\mu\nu}+f_{+}^{\mu\nu};

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So write that with the above as

ex:= fm_{\mu\nu} + fp_{\mu\nu} + fp^{\mu\nu};

(and declare your indices with position=free to allow you to have expressions where the index positions do not match up. So in full,

fm{#}::LaTeXForm("{f_{-}}").
fp{#}::LaTeXForm("{f_{+}}").
{\mu,\nu}::Indices(position=free);
ex:= fm_{\mu\nu} + fp_{\mu\nu} + fp^{\mu\nu};

to give

$$f_{-\mu\nu} + f_{+\mu\nu} + {f_{+}}^{\mu\nu}$$

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Thanks a lot. It is what I want.