/sci/ - Science & Math

>>9505555

>>8962385
I have interests in the theory of dynamical systems, the theory of functionals, real analysis, complex analysis, tensor analysis, and numerical analysis. In numerical analysis, I have an interest in developing algorithms whose error terms can be correlated with decoherence and/or violation of conservation of information in quantum theory. I have also been working on non-coordinate bases for general relativity and I think number theory is relevant to my interests in this regard.

The specific "new" thing I have been trying to break into is the analysis of hyperreal numbers. Classical field theory is extended into quantum field theory by extending the real numbers into the complex numbers and I want to study how to extend that to "hypercomplex" field theory by applying the concepts of hyperreal analysis to the real and imaginary number lines in the domain of QFT field variables. The goal in this regard is to explore the solutions to the Hamiltonian action principle that are maxima of the action. Usually the minimum action is selected because the maximum action is almost always infinity but I think I am developing a good workaround based on hyperreal numbers. I think this could equally well be a problem in dynamics or analysis.

I have a lot of well-developed applications in mathematical physics, but recently I came up with a purely mathematical application of the principles I have been struggling to make rigorous (and failing to do so because I am not a proper mathematician). In the link below I hope you find a thoughtful and well-reasoned argument against the Riemann hypothesis (that hopefully also has an application to the axial current anomaly in QCD). This is not what I consider one of my best results but it is one that can be understood without having to go into the nested references of my other papers.

>On The Riemann Zeta Function
>http://vixra.org/abs/1703.0073