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Hidden symmetries in quantum field theories from extended complex numbers

Pascal Baseilhac
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Abstract

The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A whole set of non-local conserved charges is constructed and studied in this framework. Thereby, an algebraic non-perturbative description is possible for this n-1 parameters family of quantum field theories. Known results are obtained for specific values of the parameters, especially in relation to affine Toda field theories. Different (dual)-models can then be described in this formalism.

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Pascal Baseilhac. 1999-11-10. Hidden symmetries in quantum field theories from extended complex numbers. https://doi.org/10.1142/s0217751x99001986

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