Some results in Galilei-invariant field theories
In spite of the fact that the Galilei invariance is known to be a fundamental symmetry in the nonrelativistic world, many physical phenomena we observe do not reflect this symmetry in an obvious way. We shall study this problem within the context of path integrals of a field ϕ, which satisfies a Galilei-invariant field equation, to find vacua breaking the Galilei invariance. We show that one of such vacua is the one corresponding to a trivial solution ϕ=0 and another corresponding to a kinklike solution. The stability of the later solution, however, remains unsolved in this paper. It is pointed out that to clarify the structure of the spontaneous breakdown of the Galilei invariance within the usual canonical formalism there is a fundamental problem of quantization, namely, the Fock space description in terms of the asymptotic field, which is supposed to satisfy a linear equation, may not even be possible, hence the compatibility of the LSZ formalism with the Galilei invariance cannot be taken for granted.
KeywordsPACS 03.65 Quantum theory quantum mechanics
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