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The effective Lagrangian of a classical scalar field corresponding to the vacuum expectatuion value of a quantum scalar field which displays spontaneous symmetry breaking without vacuum energy is given by

where the parameters are functions of the dimensionless scalar which maintains the invariance under the global scale transformation

but explicitly breaks the length-scale covariance. The scale transformation corresponds to conversions of the units of length, time and reciprocal mass in the same proportion, under which the numerical values of and do not change. The dimensions of and are respectively and . The inertial coupling has the dimensions and has the dimensions The scalar has the dimensions of action and is invariant under scale transformations. Its value in empty space determines the absolute scale of mass. The Lagrangian is also invariant under the transformation

The potential density is defined by

with and Its contributions to the stress-energy tensor and the equations of and are respectively

Spontaneous symmetry breaking requires that be minimum at In empty space, the equations of and are equivalent to

and the absolute scale of mass is determined by

with

For an otherwise general function the contribution to the cosmological constant from spontaneous symmetry breaking is null in empty space. As

the potential in the stress-energy tensor is proportional to In empty space, and In states that have the same as the empty space, say canonical states, the inertial coupling is determined by

The empty space is the canobical state with minimum energy.

Defining and so that and takes the form

Its minimum is given by is the maximum point of and Due to in the linear terms in the equations of and in canonical states are proportional to

with and The correspondence between and the expectation value of a scalar field associated with a quantum effective action, is set by

where is the vacuum expectation value of the scalar field in the absence of an external current and is the effective potential. As is minimum at is maximum at as required. If is canonically normalized, its mas is given by

The dimensionless scalar field defined by

is massless. The Planck mass nomalization of and is set by and so that

with and

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