# Fields with spin

Fields with spin....

Can have a field (electromagnetic, gravitational..) a "spin" or can the existence of spin be relevant in the study of field..l.so we can asign a spin to a certain field and study the functional equation of fields with "spin" and relate this "spin" to particle spin

with this word of "spin" i would mean some intrinsic property of the field similar to this of particles...

A use would be to produce for example a spin-2 description of the graviton instead of WDW equation by mean of an equation lineal and of first order in derivatives including the term d/dt and the time.

jeff
In QFT in minkowski space, fields may be viewed as consisting of particles, so a spin-j field consists of spin-j particles. For example, photons are the massless spin-1 particles making up the electromagnetic field which is thus spoken of as a massless spin-1 field. However, the notion of field is more fundamental than that of particle since the latter is an observer-dependent concept. This is seen for example in the unruh effect in minkowski space where accelerating observers will see particles where inertial observers see only the vacuum and also in regions of spacetime in which curvature is comparable to the characteristic wavelength of field quanta. It is thus more precise to speak not of particles but in a more general sense of field excitations.

Last edited:
vanesch
Staff Emeritus
Gold Member
A basic remark is maybe needed: "a field with spin" is a fancy name (well..) for a multi-component field. Like a vector field in euclidean space has 3 components at each point (and comes down to a spin-1 field!). In relativistic notation, we use 4 components, but we actually only use 3 (for a massive vector boson). Extra complications for a massless photon make us have 2 independent components, but we still write it as a 4-component field.

A spinless field is just a field with one scalar component, such as "temperature". The less intuitive aspects come in when we use half-integer spins, because we're classically not used to them, but a spin-1/2 should be a two-component field. (and it can be, for example, a Majorana field). However, in its most popular appearing it has 4 components as a Dirac spinor.

So spin of a field is nothing else but the fact that the field has multiple components, eventually combined with conditions (gauge conditions, mass conditions) reducing the number of independent components, and subject to specific transformation rules (under the Lorentz group).

cheers,
Patrick.

Originally posted by eljose79
Can have a field (electromagnetic, gravitational..) a "spin" or can the existence of spin be relevant in the study of field..l.so we can asign a spin to a certain field and study the functional equation of fields with "spin" and relate this "spin" to particle spin

with this word of "spin" i would mean some intrinsic property of the field similar to this of particles...

A use would be to produce for example a spin-2 description of the graviton instead of WDW equation by mean of an equation lineal and of first order in derivatives including the term d/dt and the time.
If all particles (within the framework of QFT) are quanta (linear, scalar, pseudoscalar, qauge etc.) of field, then what exactly do you ask?

There is a very good article on this subject from American Journal of Physics: Hans C. Ohanian, "What is spin?" 54 (6), 500-505 (1986). I don't know if it is available online anywhere.