Fields are the fundamental principles in QFT but you can start with a Lagrangian who describes a certain model and say "cool, those are the fields that exist physically". But then you can write another Lagrangian, maybe even contain the same fields, which describes the same physics. One of the most radical examples is 1 + 1D bosonization. You start with a theory that contains only fermions and ends with a theory containing only bosons. Totally equivalent to each other. Out of a bosonization is just a 2D trick. And the models of bosonization in more dimensions are punctual models. In 2D you can always do. In extra dimensions depends on the symmetry of the fields and the model itself. We have a model toy and through a transformation you change from bosons to fermions. Does not proceed ... it's all toy model. You can not know what is most fundamental. Or original. The question of bosonization also relates to integrability. There are 2D models that are integrable. That is, it is not possible to distinguish what is most fundamental. How is this possible if the fields are fundamental?

# doubt about quantum field theory

### #1

Posted 28 January 2017 - 08:44 PM

### #2

Posted 28 January 2017 - 09:26 PM

We have a model toy and through a transformation you change from bosons to fermions.

How can you get half-spin elementary stable particles starting from full-integer elementary stable particles?

If you could split particle to two new particles, they were not elementary/fundamental particles in the first place..

We have a model toy and through a transformation you change from bosons to fermions. Does not proceed ... it's all toy model.

Well, you should start from what is reality, what can be observed by naked eye:

https://www.youtube.com/watch?v=Efgy1bV2aQo

If you start from composite-boson unstable isotope, which must have full-integer spin,

it will decay be emitting gamma photon, to decrease spin by 1 unit.

Trying to get to its ground state.

f.e. U-238, has 92 protons and 146 neutrons, so it's composite-boson, with full-integer spin (0),

it's decaying to Th-234, also composite boson (spin 0),

or by double beta decay minus, also to composite boson Pu-238 (spin 0)..

So they don't need to emit any additional gamma photons.

**Edited by Sensei, 28 January 2017 - 10:23 PM.**

How To Calculate Decay Energy Of Radioactive Isotope

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### #3

Posted 16 February 2017 - 03:17 PM

Fab=[01cEx1cEy1cEz−1cEx0−BzBy−1cEyBz0−Bx−1cEz−ByBx0]{\displaystyle F_{ab}={\begin{bmatrix}0&{\frac {1}{c}}E_{x}&{\frac {1}{c}}E_{y}&{\frac {1}{c}}E_{z}\\-{\frac {1}{c}}E_{x}&0&-B_{z}&B_{y}\\-{\frac {1}{c}}E_{y}&B_{z}&0&-B_{x}\\-{\frac {1}{c}}E_{z}&-B_{y}&B_{x}&0\end{bmatrix}}}It could be more simple if you start with electromagnetic field tensors with neutrino flavours in potential scalar fields that will prove to be 1+1D

**Edited by Meter litra, 16 February 2017 - 03:52 PM.**

### #4

Posted 16 February 2017 - 07:32 PM

you have to put (math)(/math) around your formula's, but with square brackets

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