Krudak Krudak
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There seem to be two ways of defning what a vacuum is in QFT:
1. It is state $|0\rangle$ such that $$a_k|0\rangle = 0$$ for all anihilation operators $$a_k$$, with creation operators $$a_k^{\dagger}$$. Thus, it is defined in Fock space.
2. It is state $$|0\rangle$$ such that derivative $$V_{eff}'(\phi_c) = 0$$ for effective potential $$V_{eff}$$ with $$\langle 0|\hat{\phi}|0\rangle = \phi_c$$.
Two definitions do not seem to be completely compatible at first glance, but it seems that at least second definition follows from first definition when Fock space can be defined. What exactly is happening?
Or I can ask my question differently as follows:
It is known that even for Minkowski spacetime, there exist vacua other than usual Poincare-invariant vacuum often just called as vacuum. As far as my understanding goes, the usual unique Poincare-invariant vacuum locally minimizes effective potential. Do other vacua also locally minimize effective potential?
1. It is state $|0\rangle$ such that $$a_k|0\rangle = 0$$ for all anihilation operators $$a_k$$, with creation operators $$a_k^{\dagger}$$. Thus, it is defined in Fock space.
2. It is state $$|0\rangle$$ such that derivative $$V_{eff}'(\phi_c) = 0$$ for effective potential $$V_{eff}$$ with $$\langle 0|\hat{\phi}|0\rangle = \phi_c$$.
Two definitions do not seem to be completely compatible at first glance, but it seems that at least second definition follows from first definition when Fock space can be defined. What exactly is happening?
Or I can ask my question differently as follows:
It is known that even for Minkowski spacetime, there exist vacua other than usual Poincare-invariant vacuum often just called as vacuum. As far as my understanding goes, the usual unique Poincare-invariant vacuum locally minimizes effective potential. Do other vacua also locally minimize effective potential?