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Renormalizable models with simple symmetry breaking

I. Symmetry breaking by a source term

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Abstract

If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.

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  1. Deutsches Elektronen-Synchrotron DESY, Hamburg

    K. Symanzik

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  1. K. Symanzik
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Symanzik, K. Renormalizable models with simple symmetry breaking. Commun.Math. Phys. 16, 48–80 (1970). https://doi.org/10.1007/BF01645494

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