Consider a one dimensional gauge theory where the field has mass. The term,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]m^{2}A^{\mu}A_{\mu}[/tex]

is the conventional mass term. What if you find terms in your Unified Field Theory lagrangian of the form

[tex]M_{\mu\nu}A^{\mu}A^{\nu}[/tex] ?

In this case [tex]M_{\mu\nu}[/tex] is constant.

When it is not the case that

[tex]M_{\mu\nu}[/tex]

is of the form

[tex]m^{2}g_{\mu\nu}[/tex] ,

are these to be interpreted as self-interaction terms, or self-interaction terms somehow related to mass for the gauge field, or as bona fide mass terms?

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# How do you interpret quadratic terms in the gauge field in a Lagrangian?

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