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Derivation of Poincaré invariance from general quantum field theory
Author(s) -
Froggatt C.D.,
Nielsen H.B.
Publication year - 2005
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200410134
Subject(s) - physics , quantum field theory , theoretical physics , symmetry (geometry) , poincaré conjecture , degrees of freedom (physics and chemistry) , quantum , classical mechanics , mathematical physics , quantum mechanics , mathematics , geometry
Starting from a very general quantum field theory we seek to derive Poincaré invariance in the limit of low energy excitations. We do not , of course, assume these symmetries at the outset, but rather only a very general second quantised model. Many of the degrees of freedom on which the fields depend turn out to correspond to a higher dimension. We are not yet perfectly successful. In particular, for the derivation of translational invariance, we need to assume that some background parameters, which a priori vary in space, can be interpreted as gravitational fields in a future extension of our model. Assuming translational invariance arises in this way, we essentially obtain quantum electrodynamics in just 3+1 dimensions from our model. The only remaining flaw in the model is that the photon and the various Weyl fermions turn out to have their own separate metric tensors.