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Is the higgs field in space around us?

I understand it as that the higgs field has a constant value on every space time point, is that right?

And this value is the vacuum expectation value. This value is responsible for giving mass to the elementary particles, like the fermions, right?

In the Lagrangian for e fermion there is a term $g \phi_0 \bar \psi \psi$.

$g$ is the Yukawa coupling constant and $\phi_0$ is the vacuum expectation value, right?

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  • $\begingroup$ Yes, the answer is yes. I thought we already discussed here in another question from you. Is there something still not understood to you? $\endgroup$
    – wonderich
    Jan 19, 2014 at 23:59
  • $\begingroup$ ps. I will not vote you up this time, (but I won't vote people down) unless you ask something really new. $\endgroup$
    – wonderich
    Jan 20, 2014 at 0:09
  • $\begingroup$ Sorry! I just wanted to make sure I understood it. Important is the Yukawa term and the vacuum expectation value. This value is responsible for the mass of an elemantary particle. Is that right? $\endgroup$
    – user37415
    Jan 20, 2014 at 4:57
  • $\begingroup$ Yes...... why you have doubt without much confidence in your understanding? $\endgroup$
    – wonderich
    Jan 20, 2014 at 5:40
  • $\begingroup$ You are absolutely right. I should have more confidence in my understanding. I have confidence in your explanation. You have the higgs mechanism for fermions also very well explained. $\endgroup$
    – user37415
    Jan 20, 2014 at 5:51

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The answer is yes. The answer has been explained Phys SE in here and here.

"Higgs field has a constant value on every space time point (but there is a higher order perturbation around the Higgs potential)" is a remarkable fact and a true statement in the Standard Model. It is a really interesting way for physics thinking. (Well-done Nobel Physics Prize 2013.) If still having doubts, you should read the original papers in Phys Rev Lett:

(1) Broken Symmetry and the Mass of Gauge Vector Mesons

F. Englert and R. Brout

Phys. Rev. Lett. 13, 321 (1964)

(2) Broken Symmetries and the Masses of Gauge Bosons

Peter W. Higgs

Phys. Rev. Lett. 13, 508 (1964)

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