Why the kink ([tex]\phi(x)=tanh(\frac{x}{\xi})[/tex]),(adsbygoogle = window.adsbygoogle || []).push({});

can not tunnel into vacuum [tex]+v [/tex]or [tex]-v[/tex] (Spontaneous symmetry breaking vacuum).

From the boundary condition([tex]x\rightarrow \pm\infty, \phi(x)\rightarrow \pm v[/tex]),

it is self-evident.

but the book states:

Due to the infinite high energy barrier, the kink can not tunnel into the vacuum.

where is the infinite high energy barrier?

The energy density is [tex]E(x)=\frac{gv^4}{2}sech^4 (\frac{x}{\xi})[/tex],

whose integration over all space is finite.

where is the infinite high energy barrier?

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# Why Kink can not tunnel to vacuum, and is topologically stable

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