Search Results (11)

A new non-minimal version of the Einstein–Dirac-axion theory is established. This version of the non-minimal theory describing the interaction of gravitational, spinor, and axion fields is of the second order in derivatives in the context of the Effective Field Theory and is of the first order in the spinor particle number density. The model Lagrangian contains four parameters of non-minimal coupling and includes, in addition to the Riemann tensor, Ricci tensor, and Ricci scalar, as well as left-dual and right-dual curvature tensors. The pseudoscalar field appears in the Lagrangian in terms of trigonometric functions providing the discrete symmetry associated with axions, which is supported. The coupled system of extended master equations for the gravitational, spinor, and axion fields is derived; the structure of new non-minimal sources that appear in these master equations is discussed. Application of the established theory to the isotropic homogeneous cosmological model is considered; new exact solutions are presented for a few model sets of guiding non-minimal parameters. A special solution is presented, which describes an exponential growth of the spinor number density; this solution shows that spinor particles (massive fermions and massless neutrinos) can be born in the early Universe due to the non-minimal interaction with the spacetime curvature. Full article

Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be written in terms of a massless minimally coupled scalar field. The elementary fields necessary for the construction of quantum geometry are introduced and classified. A complete Krein–Fock space structure for elementary fields is presented using field operator algebras. We conclude that since quantum de Sitter geometry can be constructed by elementary fields operators, the geometry quantum state is immersed in the Krein–Fock space and evolves in it. The total number of accessible quantum states in the universe is chosen as a parameter of quantum state evolution, which has a relationship with the universe’s entropy. Inspired by the Wheeler–DeWitt constraint equation in cosmology, the evolution equation of the geometry quantum state is formulated in terms of the Lagrangian density of interaction fields in ambient space formalism. Full article

In this paper, we study the entanglement structure of a system of N quantum oscillators with distinctive coupling strengths, all linearly coupled to a common massless scalar quantum field. This study is helpful in characterizing the notion of an entanglement domain and its symmetry features, which is useful for understanding the interplay between different levels of structure in many-body quantum systems. The effect of the quantum field on the system is derived via the influence functional and the correlation functions are obtained from the solutions of the evolutionary operator of the reduced density matrix. They are then used to construct the covariance matrix, which forms the basis for our analysis of the structure of quantum entanglement in this open system. To make the physical features explicit, we consider a system of three quantum coupled oscillators placed at the vertices of an equilateral triangle with disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As a physical illustration, we apply the results for these two different configurations to address some basic issues in macroscopic quantum phenomena from the quantum entanglement perspective. Full article

An investigation has been carried out on a reconfigured form of the Einstein-Hilbert action, denoted by $f(R,T^{\varphi })$, where $T^{\varphi }$ represents the energy-momentum tensor trace of the scalar field under consideration. The study has focused on how the structural behavior of the scalar field changes based on the potential’s shape, which has led to the development of a new set of Friedmann equations. In the context of modified theories, researchers have extensively explored the range of gravitational wave polarization modes associated with relevant fields. In addition to the two transverse-traceless tensor modes that are typically observed in general relativity, two additional scalar modes have been identified: a massive longitudinal mode and a massless transverse mode, also known as the breathing mode. Full article

The Kerr/CFT correspondence provides a holographic description of spinning black holes that exist in our universe and the notion of hidden conformal symmetry allows for a formulation of this correspondence that is away from extremality. In this study, we examined how hidden conformal symmetry is manifest when we consider dynamics beyond the Klein–Gordon equation through studying the analytic structure of the higher derivative equations of the motion of a massless probe scalar field on a Kerr background, using the monodromy method. Since such higher derivative dynamics appear in known examples of holographic AdS/logCFT correspondences, we investigated whether or not a Kerr/logCFT correspondence could be possible. Full article

We classified and studied the charged black hole and wormhole solutions in the Einstein–Maxwell system in the presence of a massless, real scalar field. The possible existence of charged black holes in general scalar–tensor theories was studied in Bronnikov et al., 1999; black holes and wormholes exist for a negative kinetic term for the scalar field. Using a conformal transformation, the static, spherically symmetric possible structures in the minimal coupled system are described. Besides wormholes and naked singularities, only a restricted class of black hole exists, exhibiting a horizon with an infinite surface and a timelike central singularity. The black holes and wormholes defined in the Einstein frame have some specificities with respect to the non-minimal coupling original frame, which are discussed in the text. Full article

Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry. Full article

This work is devoted to the study of the asymptotics of the gravitational field of primary particles with nonzero rest mass. These particles are structurally composed of two closed “null strings” (thin closed tubes of a massless scalar field) in the shape of a circle, and they are formed in a gas of null strings as a result of gravitational interaction. It is shown that on time scales much larger than the time of one complete cycle of oscillation of the null strings forming a particle, or at distances much larger than the dimensions of the region within which the oscillations of interacting null strings occur, the gravitational field of such a particle is described by the Minkowski metric. It is noted that with decreasing observation time or on distance scales that are commensurate with the size of primary particles, significant deviations of the gravitational field from the flat Minkowski space-time should appear in the gas of null strings. Full article

In this paper, we investigated the possible consequences of gravitational interaction in a gas of null strings. The structural elements of this gas are closed null strings in the form of a circle (thin closed tubes of massless scalar field). A possibility to qualitatively take into account the mutual influence on motion for gravitationally interacting null strings is proposed. It is shown that the result of gravitational interaction is the self-consistent motion of two null strings inside a space-limited region. Such systems of gravitationally interacting null strings can be considered as primary particles in a gas of null strings with an effective nonzero rest mass. It is noted that the “lifetime” of such particles should depend on external conditions. Long-term existence (“lifetime”) of primary particles is possible if they are combined into more complex structures. The possibility of such a union depends on the motion direction of the null strings forming the particles. The most interesting is the possibility of combining primary particles into spherically symmetric formations—“macro” objects. A feature of such “macro” formations in a gas of null strings is the fundamental impossibility to have finally formed structure. In a gas of null strings, processes leading to a random (dynamic) change in the number of null strings gravitationally belonging to a “macro” object are inevitable. By averaging over time the various spatial distributions of the “macro” formations, the concepts of “substance” and “interaction field” can be introduced in a gas of null strings. Full article

We consider the formation of structured and massless particles with spin 1, by using the Yang–Mills-like stochastic equations system for the group symmetry $SU\left(2\right)\otimes U\left(1\right)$ without taking into account the nonlinear term characterizing self-action. We prove that, in the first phase of relaxation, as a result of multi-scale random fluctuations of quantum fields, massless particles with spin 1, further referred as hions, are generated in the form of statistically stable quantized structures, which are localized on 2D topological manifolds. We also study the wave state and the geometrical structure of the hion when as a free particle and, accordingly, while it interacts with a random environment becoming a quasi-particle with a finite lifetime. In the second phase of relaxation, the vector boson makes spontaneous transitions to other massless and mass states. The problem of entanglement of two hions with opposite projections of the spins $+1$ and $-1$ and the formation of a scalar zero-spin boson are also thoroughly studied. We analyze the properties of the scalar field and show that it corresponds to the Bose–Einstein (BE) condensate. The scalar boson decay problems, as well as a number of features characterizing the stability of BE condensate, are also discussed. Then, we report on the structure of empty space–time in the context of new properties of the quantum vacuum, implying on the existence of a natural quantum computer with complicated logic, which manifests in the form of dark energy. The possibilities of space–time engineering are also discussed. Full article

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder–Weyl variational formulation (2015–2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable $g_{\mu \nu }$ being realized by the third-order 4-tensor ${\mathrm{\Pi }}_{\mu \nu }^{\alpha }$ . It is shown that this generates a corresponding Hamilton–Jacobi theory in which the Hamilton principal function is a 4-tensor $S^{\alpha }$ . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton–Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field. Full article