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We define a modified covariant Klein-Gordon (KG) equation containing quantum vacuum contributions arising from the self-interaction of matter with its own internal kinetic energy. The modified KG equation is exemplified for a variety of vacuum fields and various properties of the equation are articulated thereof. Generalized commutation and Energy-Momentum relations are characterized for a null vacuum-phase scenario of the proposed vacuum field $lambda$. Within this limited scenario, a representation theorem is introduced suggesting that one can equally modify the spacetime structure or momentum operator in articulating the proposed quantum theory. Such a modified KG equation is further shown to eliminate infrared and the ultraviolet divergences in the generalized Klein-Gordon propagator.
Hawkings singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, there are
It is well known that the Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully re
In this paper we show that the Schrodinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.
We prove global well-posedness for the 3D Klein-Gordon equation with a concentrated nonlinearity.
The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group cor