Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Newtonian gravitational theory: Interaction with light

The interaction of light with the gravitational field of a mass point described by a Newtonian gravitational field theory gives the same gravitational red shift as accepted theory. The dual force which is an integral part of the classical field theory and which has been shown to give the same advance of the perihelion of the orbit as Einstein's General Theory of Relativity is also the reason that light is deflected in the neighborhood of a massive particle. The deflection predicted is slightly more than 10% larger than Einstein's value, but within the experimental error of observational data. The dual force and its effects must be taken seriously. Its role in electrodynamics and quantum mechanics is briefly discussed.     

A Universal Regulator?

By using the principle of metrical invariance which requires that all physical laws are independent of the choice of units (alternatively, all physical laws are invariant with respect to scale transformations of space-time coordinates) and Goldstone's theorem, a universal regulator is discovered. The cosmic field is the Yang-Mills field of the local scale transformations. Its physical role is as follows. Cosmon, its quantum, is a massless, spinless, and neutral particle. The cosmic field is created by inertial masses. Therefore it participates in all physical processes and if its presence is taken into account, then the quantum field theory is free from all ultraviolet infinities. From the point of view of Yang-Mills field theory, it is proved that the so-called gravitational masses are identical with inertial masses and the gravitational field is created by inertial masses moving non-inertially. This fact permits to solve satisfactorily the problem of energy-momentum complex of the gravitational field. The system of equations which defines simultaneously the cosmic and gravitational fields is established. A non-Einstein cosmology is outlined.     

Neutrinos in general relativity: Four(?) levels of approach

The three subsequent levels of approach to the problem of the neutrino in general relativity which have been exploited till now, are:

1. ‘classical particle’ approach, i.e. a study on the neutrino as a classical particle in a classical, given gravitational field;
2. ‘quantum particle’ approach, i.e. considering the Dirac equation for the neutrino in a given gravitational field;
3. ‘classical field’ approach comprising the study of combined neutrino-gravitational fields.

Many results obtained along these lines are presented, with emphasis upon the geometrical theory of two-component neutrino-gravitational fields. A synthesis of the particle and fields aspects of the neutrino could provide a possible fourth, till now non-existing, ‘quantum field’ level of approach. This should deal with a guantized neutrino field in a curved space-time (which might be also quantized, but perhaps this should belong already to a next, fifth level of approach). Studies on the neutrino physics in gravitational fields reveal not only a series of results which are of interest in se, and which may be used as the basis to a unified theory of neutrino and gravitational fields (the Rainich problem for the neutrino). They provide in addition the necessary material for astrophysical and cosmological applications; some of these are outlined in relation to the results presented.     

Gravitational Gauge Interactions of Dirac Field

Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge field, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.     

Quantum theory in external electromagnetic and gravitational fields: A comparison of some conceptual issues

The quantum theories of a scalar field interacting with external electromagnetic and gravitational fields respectively are compared. It is shown that several peculiar features, like the ambiguity of particle definition, thermal effects etc., which are thought to be special to quantum theory in curved spacetime, have analogues in the case of electromagnetism.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.     

An alternative quantum theory for single particles and a proposed experimental test

An alternative quantum theory for single particles bounded in the external field proposed in 1986 (Huang X. Y., Phys. Lett. A., 1986, 115: 310) is further developed from which the energy of the state for the single particle takes one of the eigenvalues of the quantum Hamiltonian, and the usual quantum mechanics for the particle in a stationary state holds only in the statistical sense. In light of the theory, the particle of definite energy, ground-state-energy for instance, can exhibit a novel periodic behavior. This result for the ground-state-energy state neutron in the Earth’s gravitational field is experimentally testable using ultracold neutron beam passing through the same apparatus that was devised in 2002 to identify the energy quantization of neutron in the field (Nesvizhevsky V. V., et al., Nature, 2002, 415: 297).      

Algebraic classification of Weyl anomalies in arbitrary dimensions

Conformally invariant systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to the Weyl invariance of classical massless field systems in interaction with gravity. In the quantum theory, the latter symmetry no longer survives: A Weyl anomaly appears. Anomalies are a cornerstone of quantum field theory, and, for the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.     

On quantum radiation in curved spacetime

In the context of quantum field theories in curved spacetime, we compute the effective action of the transition amplitude from vacuum to vacuum in the presence of an external gravitational field. The imaginary part of the resulted effective action determines the probability of vacuum decay via a quantum tunneling process, giving the rate and spectrum of particle creations. We show that (i) the gravitational field polarizes the vacuum and discretizes its spectrum; (ii) vacuum gains gravitational energy by such a polarization. On the basis of gravitational vacuum polarization, we discuss the quantum origin of vacuum decay in curved spacetime as pair-creations of particles and anti-particles. The thermal spectrum of particle creations is attributed to (i) the CPT invariance of pair-creations (annihilations) from (into) vacuum and (ii) vacuum acts as a reserve with the temperature determined by gravitational energy-gain.     

Pauli equation for a particle in metric and electromagnetic fields

A Pauli theory (Pauli equation and definition of probability current and density) for a particle in weak metric and arbitrary electromagnetic fields is treated. To formulate non-relativistic quantum mechanical problems in arbitrary electromagnetic fields and weak metrics (non-inertial systems, gravitational fields which are distant fields of arbitrary distribution of masses, gravitational waves) it is not necessary to make use of the general-relativistic Dirac equation. Close analogies to the known Pauli theory with electromagnetic fields exist. For different metric fields the corresponding Hamiltonians are given. For quantum systems (H-atoms) which are disturbed by a homogeneous gravitational field and a gravitational wave the resulting shift of energy levels and the transition probability is calculated.     

Bound states of a gravitational soliton and a test particle

Classical and quantum bound states of a test particle in the regular gravitational field of a gravitational soliton are investigated. The quantum spectrum is very similar to that of a Newtonian atom, except for the absence ofs orbitals.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton‘s theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein‘s general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.     

The Lee–Wick fields out of gravity

We study the Maxwell–Einstein theory in the framework of effective field theories. We show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a Lee–Wick vector field as an extra degree of freedom in the theory. Thus gravity provides a natural mechanism for the emergence of this exotic particle.     

Renormalization of the Weinberg-Salam Model with Local Scale Invariance

In article [1] a quantum field theory for electroweak interaction and gravitational interaction has been proposed. By introducing the conformal (Weyl) symmetry, this theory has local scale invariance and SU(2)⊗U(l) gauge invariance and leads to the existence of Weyl's vector meson, which absorbs the Higgs particle remaining in the W-S model, and other interesting results. However, it is remarked in the above paper that the theory, even if it ignores the gravitational interaction, is not renormalisable. So its application is limited.