Two approaches to anomaly-free quantization of general covariant systems on an example of a two-dimensional string

In this paper we discuss two approaches to anomaly-free quantization of a two-dimensional string. The first approach is based on the canonical Dirac prescription of quantization of degenerated systems. At the second approach we "weaken" the Dirac quantization conditions requiring the solving of first class constraints only in the sense of mean values. At both approaches there are no states with the indefinite metrics.Comment: LATEX, 14 pages, no figure

The Dynamic Quantization of Gravity and the Cosmological Constant Problem

After a brief outlook of the dynamic quantization method and application of the method to gravity the idea of natural solution of cosmological constant problem in inflating Universe is presented.Comment: 22 page

A note on the vacuum structure to lattice Euclidean quantum gravity

It is shown that the ground state or vacuum to the lattice Euclidean quantum gravity is significantly different from the ground states to the well-known vacua in QED, QCD, et cetera. In the case of the lattice Euclidean quantum gravity, the long-wavelength scale vacuum structure is similar to that in QED, moreover the quantum fluctuations to gravity are very reduced in comparison with the situation in QED. But the small scale (of the order of the lattice scale) vacuum structure to gravity is significantly different from that to the long-wavelength scales: the fluctuation values of geometrical degrees of freedom (tetrads) are commensurable with theirs most probable values.Comment: 13 page

Canonical quantization of two-dimensional gravity

A canonical quantization of two-dimensional gravity minimally coupled to real scalar and spinor Majorana fields is presented. The physical state space of the theory is completely described and calculations are also made of the average value of the metric tensor relative to states close to the ground stateComment: 26 pages, LaTe

A new approach to quantization of gravity. 2+1-dimensional example

In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general covariant theories such as gravitation, a Hamiltonian is any linear combination of the first class constraints, which can be considered as gauge transformation generators. To perform quantization, the Dirac field modes with gauge invariant creation and annihilation operators are selected. The regularization of the theory is made by imposing an infinite set of the second class constraints: almost all the gauge invariant creation and annihilation operators (except for a finite number) are put equal to zero. As a result the regularized theory is gauge invariant. The gauge invariant states are built by using the remained gauge invariant fermion creation operators similar to the usual construction of the states in any Fock space. The developed dynamic quantization method can construct a mathematically correct perturbation theory in a gravitational constant.Comment: 30 pages, LaTex, no figure

Existence of an effective fermion vertex to lattice gravity

It is shown that an effective fermion vertex arises to lattice gravity coupled with fermions. The vertices are associated with gravitational instantons, much as the effective fermion vertices arising due to the existence of fermion zero modes associated with instantons in the Yang-Mills theory.Comment: 6 pages. arXiv admin note: text overlap with arXiv:1709.10001, arXiv:1701.0217

Wilson fermion doubling phenomenon on irregular lattice: the similarity and difference with the case of regular lattice

It is shown that the Wilson fermion doubling phenomenon on irregular lattices (simplicial complexes) does exist. This means that the irregular (not smooth) zero or soft modes exist. The statement is proved on 4 Dimensional lattice by means of the Atiyah-Singer index theorem, then it is extended easily into the cases $D<4$. But there is a fundamental difference between doubled quanta on regular and irregular lattices: in the latter case the propagator decreases exponentially. This means that the doubled quanta on irregular lattice are "bad" quasiparticles.Comment: 20 pages, 3 figure

Fermion zero mode associated with instantonlike self-dual solution to lattice Euclidean gravity

We prove the existence of lattice fermion zero mode associated with self-dual lattice gravity solution.Comment: 10 page

The lattice quantum gravity, its continuum limit and the cosmological constant problem

It is shown that in the frame of discrete quantum theory of gravity constructed by S. N. Vergeles, the cosmological constant problem in inflating universe has a natural solution.Comment: 20 pages, 1 figur

Neutrino oscillations: another physics?

It is shown that the neutrino oscillations phenomenon may be attributed to the Wilson fermion doubling phenomenon. The Wilson fermion doubling exists only on the lattices, both periodic and non-periodic (simplicial complexes). Just the last case plays a key role here. Thereby, the neutrino oscillations may show for the existence of a space-time granularity.Comment: 4 pages, 3 figure