Suppose I have a field [itex]\hat{X}[/itex]...(adsbygoogle = window.adsbygoogle || []).push({});

What kind of operator should it be in order to develop a vev which doesn't break the Poincare invariance?

I am sure that a scalar field doesn't break the poincare invariance, because it doesn't transform.

However I don't know how to write it down mathematically or prove it...

Also, because I don't know how to "prove" it, I am not sure if there can exist some other [itex]X[/itex] field/operator which would keep the poincare invariance untouched after getting a vev...So why couldn't it be a fermion? or a vector field?

Is it the same as looking at the Lorentz group? So that you have the scalar in (0,0)repr, while the fermions can be in (1/2,0) or (0,1/2) and vectors in (1/2,1/2)?

But who tells me that the vacuum shouldn't be a spinor or vector?

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# Poincare Invariance of vacuum

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