Finite Quantum Theory Research Articles

Finite quantum theory of fields and strings. 1. Consistent quantization in the Stueckelberg-Feynman treatment

Finite quantum theory of fields and strings. 1. Consistent quantization in the Stueckelberg-Feynman treatment

Finite quantum theory of fields and strings. 2. Gravitational self-regularization at Planck scales

Finite quantum theory of fields and strings. 2. Gravitational self-regularization at Planck scales

Symmetries in Foundation of Quantum Theory and Mathematics

In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

Finite Mathematics, Finite Quantum Theory and a Conjecture on the Nature of Time

We first give a rigorous mathematical proof that classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a special degenerate case of finite one in the formal limit when the characteristic $p$ of the field or ring in finite mathematics goes to infinity. We consider a finite quantum theory (FQT) based on finite mathematics and prove that standard continuous quantum theory is a special case of FQT in the formal limit $p\to\infty$. The description of states in standard quantum theory contains a big redundancy of elements: the theory is based on real numbers while with any desired accuracy the states can be described by using only integers, i.e. rational and real numbers play only auxiliary role. Therefore, in FQT infinities cannot exist in principle, FQT is based on a more fundamental mathematics than standard quantum theory and the description of states in FQT is much more thrifty than in standard quantum theory. Space and time are purely classical notions and are not present in FQT at all. In the present paper we discuss how classical equations of motions arise as a consequence of the fact that $p$ changes, i.e. $p$ is the evolution parameter. It is shown that there exist scenarios when classical equations of motion for cosmological acceleration and gravity can be formulated exclusively in terms of quantum quantities without using space, time and standard semiclassical approximation.

Inflation in Gravity

Gravity is a gravitational fields model based on two symmetric tensors, gμν and , and new matter fields given by . This model has great properties at the quantum level. For example: It lives at one loop only, the classical equations of motion of the original fields are preserved and it is a finite quantum theory in the vacuum. Besides, massive particles follow an anomalous geodesic, while trajectories of massless particles are given by a null geodesic of the effective metric . In previous works, the accelerated expansion of the universe was explained without dark energy. Additionally, we saw that matter helps to explain dark matter. All these are motivations to study the effect of Gravity in Cosmic Inflation. For this, we introduce one traditional inflaton, φ, plus his partner, . Additionally, we have the contribution of gμν and .

Why superstrings?

Abstract The standard gange field theory of strong and electroweak interactions is believed to explain all known elementary particle processes up to an energy of at least 1 TeV. It is likely that this model can be enlarged to account for even higher energies, perhaps approaching the Planck scale of 1019 GeV. However, field theory offers no explanation, even in principle, of the origin of the gauge group(s), of the representations which actually occur in nature, nor of the values of the twenty odd parameters which appear in the theory. In principle, superstrings can answer these questions, and also give a finite quantum theory of gravitation. This article tries to show how this is possible, and to describe the enormity of the task being undertaken.

One-loop divergences in the quantum theory of supergravity

Supergravity does not lead to a finite quantum theory of gravitation when coupled to the spin 1, 1 2 matter multiplet. The S-matrix of photon-photon scattering diverges; its divergences are proportional to the square of the photon energy-momentum tensor, in agreement with electro-magnetic duality and chiral invariance. The graviton self-energy corrections are divergent in pure supergravity as well as in the coupled Maxwell-Einstein system and satisfy their Ward identity because the supersymmetry ghost field is commuting. The photon-graviton vertex corrections diverge, as expected from the non-invariance of the action under local scale transformations, and satisfy the equivalence principle at the quantum level. The photon self-energy is divergent.