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We quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or…
With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction $u^4_4$ we define the Wick kernel of the interacting quantum field in four-dimensional space-time and…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…
Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schroedinger's postulated wave-function rule for the operator quantization of the particle's canonical three-momentum, taken together with…
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…
It is shown that any theory of gravitation, based on the hypothesis of the geodesic motion of test particles must be invariant under geodesic (projecive) mappings of the used space-time. The reason is that due to invariance of the equations…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling…
The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang--big crunch) at the quantum…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…