Generalized uncertainty principles and quantum field theory
Viqar HusainDepartment of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, CanadaDawood KothawalaDepartment of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, CanadaSanjeev S. SeahraDepartment of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada
2013en
ABI
Abstract
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\stackrel{^}{x},\stackrel{^}{p}]=if(\stackrel{^}{p})$. We apply this deformed quantization to free scalar field theory for ${f}_{\ifmmode\pm\else\textpm\fi{}}=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\beta}{p}^{2}$. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green's function for ${f}_{+}$ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for ${f}_{\ensuremath{-}}$ such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths.
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