Analyzing free quantum field theories on the ax + b space-time and Wigner contractions to the Minkowski plane
LeBlanc, Maurice Joseph
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While much work toward constructing quantum field theories has already been done in the case of a flat space-time, the discipline is not nearly as well-developed in the case of a curved space-time. The axioms offered by Wightman provide a mathematically rigorous system for the construction of a quantum field theory on Minkowski space. I extend this axiomatic approach in order to develop a model for a free scalar quantum field theory in the case of a two-dimensional curved space-time by offering a set of axioms for a quantum state field which can then be used to create a quantum operator field by second quantization using the Segal field operator. I then demonstrate an example of a mathematically rigorous free scalar quantum field theory on a curved space-time satisfying these axioms. Finally I use Wigner's contraction method to demonstrate that these free quantum fields on the curved ax+b space-time limit to certain quantum fields on the flat plane, R^2.