Abstract
Considering the phenomenological studies of non-linear quantum models, we use an axiomatic approach to modify the Dirac Lagrangian. We apply constraints such as Hermiticity, locality, universality, etc to obtain various generic modified energy dispersion relations. After-which, we use the parameters from the neutrino oscillations to obtain bounds on these new modified dispersion relations.
Highlights
MotivationThe usefulness of non-linear equations could be seen in quantum cosmology, where a weak non-linearity could replace the Big Bang singularity with a bounce [1]
The usefulness of non-linear equations could be seen in quantum cosmology, where a weak non-linearity could replace the Big Bang singularity with a bounce [1]. This motivates us to ask if a similar generalisation with the Dirac equation could be used to model new physics
In finding the new equations of motion, we use the Lagrange multiplier method1. This simultaneously minimizes the information measure and gives us a generalized Dirac equation. We can interpret these non-linear Dirac equations as encoding potential new physics at higher energies
Summary
The usefulness of non-linear equations could be seen in quantum cosmology, where a weak non-linearity could replace the Big Bang singularity with a bounce [1]. This motivates us to ask if a similar generalisation with the Dirac equation could be used to model new physics. In finding the new equations of motion, we use the Lagrange multiplier method1 This simultaneously minimizes the information measure and gives us a generalized Dirac equation. We can interpret these non-linear Dirac equations as encoding potential new physics at higher energies. It is important to note that the non-linearity here is not demanded but a result of information theoretic generalisation [3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
