Wednesday, 8 July 2015

Are there solitary waves in phi4 theory in 3+1 dimensions?


In 3+1 dimensions with signature +1 -1 -1 -1,


L=12μϕμϕϕ2/2ϕ4/4


field equation: ϕ+ϕ+ϕ3=0

(check this)


=2t2


Note that it is not a Mexican hat. I guess this haven't been solved exactly before but, somebody have shown or discarded that there could be soliton solutions or at least solitary waves?




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