On Jun 14, 11:23 am, Barrow wrote:
Dear all,
Why is the degree of freedom of a scalar field equal to 1?
Why does the massless photon(vector boson) have degrees of freedom
2? and Why is the massive photon degrees of freedom equal to 3??

I don't figure out any physical meaning of the above facts.
Actually, I read these from the introduction of higgs phonemena from
the text book by Mr. Ryder. Any instructions will be appreciated!
Sincerely Barrow

The scalar having just one degree of freedom is true by definition.
Scalars are defined as just numbers.

A vector boson, on the other hand, has at most three degrees of
freedom, corresponding to the three independent directions in which it
might be polarized. Those correspond to two independent transverse
degrees and one longitudinal degree of freedom, defined as
oscillations perpendicular or parallel to the direction of wave
motion, respectively. Massless gauge particles obey the Coulomb gauge
condition del dot A = 0. This is equivalent to saying k dot A = 0,
where k is the wave number vector. This says that k must be
perpendicular to A at all points and hence the wave is transverse, and
consists of only two degrees of freedom. The gauge condition for a
massive particle has del dot A being proportional to the particle's
mass. So the massive particle corresponds to a wave having both
transverse and longitudinal components, hence three degrees of
freedom.