- #1
QuantumSkippy
- 18
- 1
Hi Everyone!
I have been told that even for an entirely LOCAL scalar field φ with Lagrangian density say of the form,
L = ∂/∂xμ∂/∂xμφ ± φ4 + Aφ3 + Bφ2. +. Cφ + D,
that it is really bad, bad, bad because the coefficient (C) of φ is not zero!
That is, ∂/∂φ(L) ≠ 0 when φ = 0 is very bad because the vacuum will not be stable as a result of the fact that the minimum value of φ is not zero. They are even saying that the particles of this field cannot be real physical particles!
I can certainly see this for the Higgs Field which is supposed to be everywhere in the Universe. It is a big deal in that case.
My point is, how does this matter much for AN ENTIRELY LOCAL FIELD, as an entirely local field comes into and out of existence as and when? Why does it matter if it's minimum is not zero, if it only exists for 10-15 seconds, or whatever, coming into existence whenever and going out of existence whenever?
Please let me know what is the go here! Please supply references wherever you can; I can then chase them up and I will then LEARN!
How does it matter for an entirely local field?
Thanks in advance or all your help. Please impress me with your knowledge!
I have been told that even for an entirely LOCAL scalar field φ with Lagrangian density say of the form,
L = ∂/∂xμ∂/∂xμφ ± φ4 + Aφ3 + Bφ2. +. Cφ + D,
that it is really bad, bad, bad because the coefficient (C) of φ is not zero!
That is, ∂/∂φ(L) ≠ 0 when φ = 0 is very bad because the vacuum will not be stable as a result of the fact that the minimum value of φ is not zero. They are even saying that the particles of this field cannot be real physical particles!
I can certainly see this for the Higgs Field which is supposed to be everywhere in the Universe. It is a big deal in that case.
My point is, how does this matter much for AN ENTIRELY LOCAL FIELD, as an entirely local field comes into and out of existence as and when? Why does it matter if it's minimum is not zero, if it only exists for 10-15 seconds, or whatever, coming into existence whenever and going out of existence whenever?
Please let me know what is the go here! Please supply references wherever you can; I can then chase them up and I will then LEARN!
How does it matter for an entirely local field?
Thanks in advance or all your help. Please impress me with your knowledge!