Scalar field and spin 1/2 field

[captain]

are bosons represented by a scalar field and fermions represented by a spin 1/2 field or how does it work?

 

[strangerep]

are bosons represented by a scalar field and fermions represented by a spin 1/2 field or how does it work?

Bosons have integer spin (0,1,2...). Fermions have half-integer spin (1/2, 3/2, ...)

 

[captain]

Bosons have integer spin (0,1,2...). Fermions have half-integer spin (1/2, 3/2, ...)

does that mean a scalar field is a spin zero field or is it an integer spin field?

 

[Son Goku]

does that mean a scalar field is a spin zero field or is it an integer spin field?

A scalar field is a spin zero field. For spin one you'd need a vector field and for spin two you'd need a second rank tensor field.

 

[captain]

A scalar field is a spin zero field. For spin one you'd need a vector field and for spin two you'd need a second rank tensor field.

what about a spin 1/2 or spin 3/2?

 

[Son Goku]

what about a spin 1/2 or spin 3/2?

A spin-1/2 particle is described using a Lorentz/Dirac Spinor Field. There are no “fundamental” spin-3/2 particles so the field that would describe it isn’t used that often. However if you know representation theory you can easily see what the field’s properties are like.

Also there are difficulties in taking spin-3/2 theories further than second order in perturbation theory, which is one of the reasons for the field formalism.

 

[captain]

is there a different propagator for each spin field?

 

[Son Goku]

is there a different propagator for each spin field?

Yes, there is a different propagator for each field as they have different Hamiltonians. There is also a different Feynman propagator for each free particle species of a given spin.*

*Obviously there are also different propagators for interacting theories, but their analytic forms aren’t known.