Which particles can have vacuum expectation values and why?

[gasar8]

Homework Statement

Can someone explain to me what particles (fermions, scalar/vector bosons, gravitons, ...) can have their vacuum expectation values and why? Which components of these fields can have VEV-s?

The Attempt at a Solution

I am assuming only scalar boson fields have it (like Higgs field) and give masses to other particles, but I don't know why. Is there symmetry involved? I can imagine which components can have VEVs in simple mexican hat - shaped potentials, where you can choose only one minimum, but I am asking this because I am into minimal left-right symmetry, where I have two triplets and a bi-dublet and I am not sure which components I can neglect.

 

[Asim Riaz]

The vacuum expectation value (VEV) of a particle is its average value in the vacuum. It is a measure of the particle's "background" value and is usually calculated by taking the average over all space-time points. Certain particles, such as scalar bosons (e.g. the Higgs field), can have non-zero VEVs. In this case, the particle's VEV is related to its mass. The components of a field that can have non-zero VEVs depend on the form of the potential. For example, in a Mexican-hat type potential, the minimum of the potential corresponds to the VEV of the field. On the other hand, vector bosons and gravitons cannot have non-zero VEVs because they have no mass and therefore cannot have a minimum value.