Scalar field and spin 1/2 field

In summary, bosons have integer spin and are represented by a scalar field, while fermions have half-integer spin and are represented by a spin 1/2 field. A scalar field is a spin zero field, while for spin one you would need a vector field and for spin two you would need a second rank tensor field. For spin-1/2 particles, a Lorentz/Dirac Spinor Field is used, and for spin-3/2 particles, the field formalism is not used often due to difficulties in taking the theory further than second order in perturbation theory. Each spin field has a different propagator, with different Hamiltonians and Feynman propagators for interacting theories.
  • #1
captain
164
0
are bosons represented by a scalar field and fermions represented by a spin 1/2 field or how does it work?
 
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  • #2
captain said:
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, ...)
 
  • #3
strangerep said:
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?
 
  • #4
captain said:
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.
 
  • #5
Son Goku said:
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?
 
  • #6
captain said:
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.
 
  • #7
is there a different propagator for each spin field?
 
  • #8
captain said:
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.
 

1. What is a scalar field?

A scalar field is a physical quantity that has a single value at each point in space. It can be thought of as a mathematical function that assigns a scalar value (such as temperature or pressure) to every point in a physical space.

2. What is a spin 1/2 field?

A spin 1/2 field is a type of quantum field that describes particles with a spin of 1/2, such as electrons. Spin is a fundamental property of particles that determines their angular momentum and behavior under certain physical interactions.

3. How are scalar fields and spin 1/2 fields related?

Scalar fields and spin 1/2 fields are both types of quantum fields that describe different properties of particles. While scalar fields describe scalar quantities like temperature or pressure, spin 1/2 fields describe the spin property of particles.

4. What is the significance of spin 1/2 fields in physics?

Spin 1/2 fields are significant in physics because they describe fundamental particles, such as electrons, that make up the building blocks of matter. Understanding the behavior of these particles is crucial in understanding the physical world.

5. How are scalar fields and spin 1/2 fields observed or measured?

Scalar fields and spin 1/2 fields cannot be directly observed or measured, as they are quantum fields that exist in the theoretical realm. However, their effects can be observed and measured through experiments and observations of the particles they describe.

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