Quantum numbers of a field acquiring vacuum expectation value

[krishna mohan]

Why should symmetries require a field that acquires vacuum expectation value to have the same quantum numbers as the vacuum? Please give me a reference also..if possible...

[javierR]

If the vacuum (without the v.e.v. of the field) has certain symmetries dictated be observation, such as local Lorentz invariance and lack of electric charge, then the presence of the field v.e.v. should not ruin these properties. Otherwise you wouldn't have demanded those symmetries of the original vacuum. That's why condensations of neutral scalars and neutral, Lorentz-scalar groupings of fermions are allowed in the Standard Model.

[RedX]

That's why condensations of neutral scalars and neutral, Lorentz-scalar groupings of fermions are allowed in the Standard Model.

So how does one explain the vector meson?

Scalar mesons, such as the pion, are condensations of a colorless, Lorentz-invariant, quark/antiquark composite fields.

If there is a similar condensation (i.e., symmetry-breaking) that leads to a vector meson, then Lorentz-invariance would be broken.

So it seems that only scalar mesons should exist, and vector mesons violate Lorentz invariance because they would spontaneously break it?