Why gauge bosons, but no gauge fermions

Click For Summary
SUMMARY

The discussion centers on the nature of gauge bosons and the absence of gauge fermions in quantum field theory. Participants clarify that gauge invariance necessitates the use of vector fields, which correspond to particles with integer spin, thus classifying them as bosons. The conversation also touches on supersymmetry, where fermions can be associated with gauge bosons, referred to as "gauginos," but their contributions are significantly weaker due to the exclusion principle. The distinction between vector and tensor fields is highlighted, particularly in relation to gravity, which is identified as a tensor field with spin 2.

PREREQUISITES
  • Understanding of gauge invariance in quantum field theory
  • Familiarity with vector and tensor fields, including their properties
  • Basic knowledge of supersymmetry and its implications for particle physics
  • Concept of spin statistics and its relevance to particle classification
NEXT STEPS
  • Study the principles of gauge invariance in quantum mechanics
  • Learn about the role of vector and tensor fields in quantum field theory
  • Explore the concept of supersymmetry and its implications for particle interactions
  • Investigate the mathematical foundations of spin and group theory in physics
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, particle physics, and theoretical physics, will benefit from this discussion, as well as students seeking to understand the fundamental interactions of particles.

Edgardo
Messages
706
Reaction score
17
Hello all,

from Marlon's journal, I read the question "DO YOU KNOW WHY FORCE CARRIERS ARE ALWAYS BOSONS ? WHY DON'T WE HAVE GAUGE FERMIONS ?"

Can anyone answer this question? :redface:
 
Physics news on Phys.org
Give me an example of a fermionic first class system,field theory,of course...

Daniel.
 
Gauge invariance involves correcting problems caused in quantum mechanics by the appearance of the partial derivatives with respect ot x,y,z,t. These partials form a relativistic 4-vector. This requires 4-vector fields so that (in EM)
d/dx-->d/dx-ieA_x, etc. The particle excitations of vector fields have spin one.
So the requirement that gauge particles (the excitations of the gauge fields) must be vector particles follows from the fact that space-time is 4 dimensional.
 
I thought that because the exchange particles must be able to carry integer spin they must be bosons. (Spin flips and all).
Josh
 
Why would they have to carry integer spin...?

Daniel.
 
Edgardo said:
Hello all,

from Marlon's journal, I read the question "DO YOU KNOW WHY FORCE CARRIERS ARE ALWAYS BOSONS ? WHY DON'T WE HAVE GAUGE FERMIONS ?"

Can anyone answer this question? :redface:

good question...

there are several ways to answer this : spin statistics being one of them

marlon :approve:
 
Meir Achuz said:
Gauge invariance involves correcting problems caused in quantum mechanics by the appearance of the partial derivatives with respect ot x,y,z,t. These partials form a relativistic 4-vector. This requires 4-vector fields so that (in EM)
d/dx-->d/dx-ieA_x, etc. The particle excitations of vector fields have spin one.
So the requirement that gauge particles (the excitations of the gauge fields) must be vector particles follows from the fact that space-time is 4 dimensional.

I like that answer :-) As gauge fields have to appear in the covariant derivative, they have to be vector fields. Nice.

cheers,
Patrick.
 
In SuperSymmetry, maybe you will call the Fermions in the same doublet with the Bosons "Gauge Fermions", because they transform together with the gauge bosons, for
example wino or zino (they form chargino and neutrino).
 
Meir Achuz said:
Gauge invariance involves correcting problems caused in quantum mechanics by the appearance of the partial derivatives with respect ot x,y,z,t. These partials form a relativistic 4-vector. This requires 4-vector fields so that (in EM)
d/dx-->d/dx-ieA_x, etc. The particle excitations of vector fields have spin one.
So the requirement that gauge particles (the excitations of the gauge fields) must be vector particles follows from the fact that space-time is 4 dimensional.

This is indeed a great answer

marlon
 
  • #10
wangyi said:
In SuperSymmetry, maybe you will call the Fermions in the same doublet with the Bosons "Gauge Fermions", because they transform together with the gauge bosons, for
example wino or zino (they form chargino and neutrino).

"Gauge Fermions" in supersymmetry are generically called "gauginos".
As long as I know, in supersimetric models they contribute with the forces just like regular gauge bosons, but because of the exclusion principle their net effect is not very strong, which also shows that if we only had "gauge fermions" and no "gauge bosons" the world wouldn't be as we know it at all.
 
Last edited:
  • #11
Meir Achuz said:
Gauge invariance involves correcting problems caused in quantum mechanics by the appearance of the partial derivatives with respect ot x,y,z,t. These partials form a relativistic 4-vector. This requires 4-vector fields so that (in EM)
d/dx-->d/dx-ieA_x, etc. The particle excitations of vector fields have spin one.
So the requirement that gauge particles (the excitations of the gauge fields) must be vector particles follows from the fact that space-time is 4 dimensional.

Unless "vector particle" means something else than the quanta of a vector field,that conclusion is incorrect.

Daniel.
 
  • #12
I am not a QFTist and know only a bit of it,so let me ask-----does gravity have to necessarily be a gauge field?If so why?
 
Last edited:
  • #13
Gravity is a gauge field.It's not a vector field (spin 1),but a tensor field (spin 2)...It's the idea behind post #11.

Daniel.
 
  • #14
Yeah ok,gravity is a gauge field(only potential differences matter).But some more stupid questions--why does a tensor field have to be spin 2 and vector field spin one?
 
Last edited:
  • #15
Aaa,nice question.:smile:Group theory.Vectors are \left(\frac{1}{2},\frac{1}{2}\right) irreducible reps of the restricted homogenous Lorentz group and therefore have total spin \frac{1}{2}+\frac{1}{2}=1.

Symmetric 2-nd rank tensors (the gravity field h_{\mu\nu} which is the I-st order perturbation expansion of GR metric g_{\mu\nu}) are (1,1)\oplus (0,0) irredcible reps of the restricted homogenous Lorentz group and have spin 1+1=2.

Daniel.
 
  • #16
put it in a language that's more comprehensible
 
  • #17
I honestly can't."Spin" means group theory.Vectors & tensors mean group theory.That's all there is to it...All u need to understand is the 'coupling' between spin & Lorentz group...

Daniel.
 
  • #18
gptejms said:
put it in a language that's more comprehensible

Quantum spin is a new concept. That means it can't really be explained in terms of older concepts. If you don't want to learn the group theory definitions, you can just accept the fact that the states of spin 1/2 only turn half as fast as the coordinates do when you perform a rotation.
 
  • #19
Agreed with Dexter.

Although in Supersymmetry the fundamental axioms of Lie algebra are modified (into.. surprise Super Lie Algebra), which is why you can have 'gauge' fermions with the same standard model quantum numbers, and they do indeed participate. However for technical reasons they have to be Majorana fermions, and when you calculate the beta function you end up with a fraction of the contribution as the gauge boson (tho not too small, maybe an order of magnitude less). Of course super symmetry is badly broken, and depending on the mechanism choice, will reduce things further.
 
  • #20
selfAdjoint said:
If you don't want to learn the group theory definitions, you can just accept the fact that the states of spin 1/2 only turn half as fast as the coordinates do when you perform a rotation.

SU(2) you mean--i know that.please complete the argument.
 
  • #21
dc: What does your sentence "Unless 'vector particle' means something else than the quanta of a vector field,that conclusion is incorrect."
in post #11 mean? I thought I had written that VPs were the quanta of VFs.

re: post #13: Can you describe how a tensor field can be a gauge field?
You and I must be talking about different kinds of "gauge field".
Mine is related to LGI in QM and gauge invariance of a theory.
 
  • #22
In that case,concluding that gauge bosons must be vector bosons is incorrect...

I didn't assert that "a tensor field can be a gauge field".I said that (not literally) "gravity,which is symmetric 2-nd rank tensor field,is a gauge field".And there are many more 4D field theory examples ,actually counterexamples to your conclusion formulated in post #3 & quoted by me in post #11.


Daniel.
 
  • #23
what's local gauge invariance in gravity theories?
 
Last edited:
  • #24
HE action is invariant under a set of local diffeomorphisms which can be shown to be the Lagrangian infinitesimal gauge transformations.Since the Hamiltonian formalism for GR is a real pain in the a$$,the analysis is simpler using Einstein's linearized theory (which uses the I-st order perturbations h_{\mu\nu} mentioned earlier).

Daniel.
 
  • #25
gptejms said:
what's local gauge invariance in gravity theories?

Hmmmm,u changed your post. :wink: There's no difference to other theories wrt the definition of "local gauge invariance".Basically,it's a I-st class system which is called "classical gravity" and is based upon the HE action...

Daniel.
 
  • #26
dextercioby said:
Why would they have to carry integer spin...?

Daniel.
I was thinking about that all fundamental interactions have interaction particles that are integer spins(photon, W,Z,and graviton?).

One question I do have(pardon my ignorance on gauge theory please) is that if gauge theory is developed to better understand fundamental interactions, why do we consider adding a half integer spin interaction particle when we do not see evidence of them(as far as I know)?

Josh
 
  • #27
joshuaw said:
I was thinking about that all fundamental interactions have interaction particles that are integer spins(photon, W,Z,and graviton?).

One question I do have(pardon my ignorance on gauge theory please) is that if gauge theory is developed to better understand fundamental interactions, why do we consider adding a half integer spin interaction particle when we do not see evidence of them(as far as I know)?

Josh

What half-integer interaction particle are you speaking of?
 
  • #28
dextercioby,
If you replace the words 'local gauge invariance' by 'invariance under a set of local diffeomorphisms',you sound impressive but you are not explaining anything.
 
  • #29
I know,but those transformations are called that way.Diffeomorphisms are typical to GR only.If u choose another I-st class theory,the Lagrangian infintiesimal gauge transformations will look differently...

Daniel.
 
  • #30
I think none of my questions is one that can not be answered in a physically intuitive manner--though it may require a better understanding than the one at just a mathematical level.I repeat my questions with the hope that one of you answers them without resorting to terms like 'local diffeomorphism' and '(1/2,1/2) irreducible representations of restricted homogeneous Lorentz group'.

Why does a vector field have spin 1?Why does gravity which is a tensor field have spin 2 quanta?When is it supposed to be spin 3 or higher?Does it go with the rank of the tensor?
What's local gauge invariance in gravity theories---can anyone explain it in physical terms?
 

Similar threads

Graduate Massive gauge bosons in QFT in/out states
  • · Replies 60 ·
3
Replies
60
Views
5K
Undergrad Two hydrogen atoms and Pauli's exclusion principle
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Bosonization Formula and its Effects on Fermion Number
  • · Replies 5 ·
Replies
5
Views
2K
High School Are bosons always their own antiparticle
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Anti-commutation relation for quantized fields
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Particles of matter as Bosons?
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Why do we use BRST in Yang Mills and where does it come from?
  • · Replies 3 ·
Replies
3
Views
2K
High School How does exchange of elementary particles result in a force?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Is it possible to have a spin chain with both bosons and fermions interacting?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Spin change of Fermions and quantum energy spectrum
  • · Replies 1 ·
Replies
1
Views
1K