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Static finite energy solutions of a classical field theory with positive mass-square

Authors:	Avinash Khare

Institution:	(1) Institute of Physics, A/105 Saheed Nagar, 751007 Bhubaneswar, India

Abstract:	Static finite energy solutions of the field theory described by $\mathcal{L} = \frac{1}{2}\partial _\mu \phi \partial _\mu \phi - ({{m^2 } \mathord{\left/ {\vphantom {{m^2 } 2}} \right. \kern-\nulldelimiterspace} 2})\phi ^2 (1 - ({{\lambda \phi ^2 } \mathord{\left/ {\vphantom {{\lambda \phi ^2 } {4m^2 }}} \right. \kern-\nulldelimiterspace} {4m^2 }}))^2$ are obtained. Some of the interesting features of this model are (1) the mass-square here is positive unlike in the λφ⁴ Higg's model, (2) the potential has three global minimas, (3) the spectrum is bounded from below unlike in the λφ⁴ theory with λ<0, (4) there are two kink and two antikink solutions, (5) unlike sine-Gordon and λφ⁴ models here there are two particles with masses m and 2m. Nontopological finite energy solutions have also been obtained for gφ ⁶ field theory with g < 3λ ² / 16m ².

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