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The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

state axiom of quantum mechanics: "physical states are described by vectors of a Hilbert space, i.e. physical states are mapped injective onto the radiances of a Hilbert space."quantum gravity is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics.

The Higgs boson combines the existence of mass together with the action of the weak force. But why it provides especially to the quarks that much mass, is still a mystery.

"Indeed there is no observation concerned with the geometrical shape of a particle or even with an atom." (E. Schrödinger)

                   Mass is essentially the manifestation of the vacuum energy

The Standard Model of Elementary Particles (SMEP), including the Higgs mechanism, is concerned with gauge theory and variational principles (energy and operator norm minimization problems), whereby each of the 4 (observed) Nature forces are related to a specific gauge group. The model does not provide any explanation where the related elementary "particles" are coming from (or have been generated out of "first mover" resp. out of mass-less photons) during the inflation phase of current big bang assumption and why their mass have their specific values. We propose an alternative mathematical framework, which replaces gauge theory and variational principles (with its underlying concept of exterior derivatives and tensor algebra) by (distributional) Hilbert scales (enabling an inner product) and variational principles. As a consequence, the vacuum energy becomes an intrinsic part of the variational principles, i.e. is identical for all considered Lagrange resp. Hamiltonian mechanisms, while the corresponding "force" becomes an observable of the considered minimization Problem.

The new technical element is a change in the underlying Hilbert space framework, i.e. the standard L(2)-Hilbert space framework is replaced by the distributional Hilbert space H(-1/2). This has two immediate consequences

- an alternative Schrödinger momentum operator can be defined, whereby the complementary closed space H(-1/2)-H(0) enables an alternative way to model "wave functions" of the ground state energy resp. condensates, superfluids & superconductivity (J. F. Annett)

- an alternative Dirac function model can be defined, whereby the regularity of the "defining" H(-1/2) Hilbert space is (now) independent from the space dimension "n" and, at the same time, more regular than the Dirac distribution "function" itself even for the space dimension n=1 (!!). In other words, an alternative modelling framework for current "physical" applications of the Dirac "function" is provided with (slightly, but essentially) reduced mathematical model required regularity assumptions to current state of the art theory, which is now (newly) independent from the mathematical model`s space-time Dimension

   

Braun K., An alternative Schrödinger momentum operator enabling a quantum gravity model

         

Braun K., Comparison table, math. modelling frameworks for SMEP and GUT

                                             

Riesz operators and rotations