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I am reading the book ‘Introduction to Particle Physics’ by Martin and Halzen. In the section about the Higgs Field the book considers the scalar field that interacts with a vector field. Using certain transformations a mass like term appears for the vector field. My doubt is that it was never explained why a scalar field was chosen for the Higgs Field and can the same be done using a bispinor Lagrangian?

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  • $\begingroup$ Related question $\endgroup$ – Aaron Stevens Apr 1 at 11:47
  • $\begingroup$ When you ask, "Can the same be done using a bispinor Lagrangian," what specifically do you mean by "the same"? Do you mean, "Can a bispinor Higgs field explain experimental data to the same accuracy and precision as a scalar Higgs field?" Or do you mean, "Can a bispinor Higgs field make the same predictions as a scalar Higgs field?" The distinction is important because those two questions may have opposite answers. $\endgroup$ – probably_someone Apr 1 at 12:08
  • $\begingroup$ @probably_someone yes $\endgroup$ – Manvendra Somvanshi Apr 1 at 14:07
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    $\begingroup$ @ManvendraSomvanshi "Yes" doesn't make a whole lot of sense as an answer to "what do you mean by this question?" Do you mean the first version of the question? The second version of the question? Both? Or something else entirely? $\endgroup$ – probably_someone Apr 1 at 14:12
  • $\begingroup$ @probably_someone I am sorry, I meant that can bispinor Higgs Field explain the experimental data. $\endgroup$ – Manvendra Somvanshi Apr 1 at 14:34
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The Higgs field is a Lorentz scalar because it needs to get a vev:

$$\langle{\Phi(x)\rangle} = v$$

which is the same in all frames. If the Higgs was in a spinor, vector or any other non-trivial Lorentz representation, it would not be possible to assign a non-zero vev to it.

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