Editing Canonical quantization (section)

===Condensates===

The construction of the scalar field states above assumed that the potential was minimized at {{mvar|φ}} = 0, so that the vacuum minimizing the Hamiltonian satisfies {{math|1=⟨''φ''⟩ = 0}}, indicating that the [[vacuum expectation value]] (VEV) of the field is zero. In cases involving [[spontaneous symmetry breaking]], it is possible to have a non-zero VEV, because the potential is minimized for a value  {{mvar|φ}} = {{mvar|v}} .  This occurs for example, if {{math|''V''(''φ'') {{=}} ''gφ''<sup>4</sup> − 2''m''<sup>2</sup>''φ''<sup>2</sup>}} with {{math|''g'' > 0}} and {{math|''m''<sup>2</sup> > 0}}, for which the minimum energy is found at {{math|''v'' {{=}} ±''m''/{{radic|''g''}}}}. The value of {{mvar|v}} in one of these vacua may be considered as ''condensate'' of the field {{mvar|φ}}. Canonical quantization then can be carried out for the ''shifted field'' {{math| ''φ''(''x'',''t'') − ''v''}}, and particle states with respect to the shifted vacuum are defined by quantizing the shifted field.  This construction is utilized in the [[Higgs mechanism]] in the [[standard model]] of [[particle physics]].