Re: spin value and energy requirement for quantum field?

I'm not quite sure what you're asking.  The field does not carry
spin; spin is the intrinsic angular momentum carried by particles
which are quantized excitations of the field.
 http://en.wikipedia.org/wiki/Spin_%28physics%29

So, for example, the photon and gluon are massless spin-1 particles.
This is a brief way of saying that if the photon's angular momentum is
measured along some direction, the result will be +1 or -1 times the
reduced Planck constant, h-bar.  Similarly, the hypothetical graviton
is a massless spin-2 particle.  The Higgs boson is a massive spin-0
particle.  The electron is a massive spin-1/2 particle.
 http://en.wikipedia.org/wiki/Photon
 http://en.wikipedia.org/wiki/Gluon
 http://en.wikipedia.org/wiki/Higgs_boson
 http://en.wikipedia.org/wiki/Electron

There is no "energy from the spin".  The minimum energy of a photon is
zero (as the wavelength goes to infinity), despite the fact that the
spin is always 1 h-bar.  The minimum energy of an electron is its mass
times the speed of light squared (when it is at rest), regardless of
its spin of 1/2 h-bar.  If there are no particles in a region of space,
then there is no spin angular momentum in that region either.

The photon particle has spin 1 because the vector potential field, of
which the photon is a quantized excitation, is a vector field.  That
means that the field transforms under Lorentz transformations
(rotations and boosts) like the space-time four-vector (t,x,y,z) and
the field carries one Lorentz index.
 http://en.wikipedia.org/wiki/Electromagnetic_four-potential
 http://en.wikipedia.org/wiki/Four-vector

The graviton particle has spin 2 because the metric tensor field, of
which the graviton is a quantized excitation, is a rank-2 tensor.
That means that the field transforms like the outer product of two
four-vectors and the field carries two Lorentz indices.
 http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29
 http://en.wikipedia.org/wiki/Lorentz_covariance

The Higgs field, of which the Higgs boson is a quantized excitation,
is unique in the Standard Model of Particle Physics.  For all other
fields (e.g. vector potential field, electron field, etc.) the lowest
energy configuration is no field at all.  For the Higgs field, the
lowest energy configuration is to fill space with the Higgs field.
Setting the Higgs field to zero would require energy.  Even though
space is filled with the Higgs field, it is not easy to produce
excitations of the field which are the spin-0 Higgs bosons.  In fact,
the Higgs boson was not produced until 2011 in the Large Hadron
Collider.
 http://en.wikipedia.org/wiki/Large_Hadron_Collider


--Randall J. Scalise
 http://www.physics.smu.edu/scalise