On the Geometric Unification of Gravity and Dark Energy

In the framework of Finslerian geometry, we propose a geometric unification between traditional gauge treatments of gravity, represented by a metric field, and dark energy, which arises as a corresponding gauge potential from the single SU(2) group. Furthermore, we study the perturbation of gravitational waves caused by dark energy. This proposition may have far reaching applications in astrophysics and cosmology.     

Time Quanta

Secondary quantizing of the “passive mass” of an isotropic and uniform nonstationary scalar field is realized, and the intensity of quantum emission of the massless scalar field is calculated for spontaneous transitions of the effective Planck particle in the line energy spectrum of the primordial Lema?tre atom. It is shown that the scalar-field quanta in the effective Riemann space can manifest themselves as time quanta of the real Minkowski space.     

Quanta and coherent states

The quantum harmonic oscillator can be considered as a composite system of indistinguishable Bose-Einstein symmetric two-level-systems (quanta). In analogy to the classical Poisson limit theorem, we show that a coherent state is the limit of a sequence of homogeneous product states (coherent spin states) and discuss statistical properties of the quanta in classical and nonclassical states.     

Facts,Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.     

从电磁统一到电弱统一

概括介绍从“电磁统一”到“电弱统一”的研究历程，并指出这一研究的科学意义以及可能给予后继研究者在科研方法上的启示．     

Gravitational and Electroweak Unification

Einstein suggested that a unified field theorybe constructed by replacing the diffeomorphisms (thecoordinate transformations of general relativity) withsome larger group. We have constructed a theory that unifies the gravitational and electroweakfields by replacing the diffeomorphisms with the largestgroup of coordinate transformations under whichconservation laws are covariant statements. Thisreplacement leads to a theory with field equations whichimply the validity of the Einstein equations of generalrelativity, with a stress-energy tensor that is justwhat one expects for the electroweak field andassociated currents. The electroweak field appears as aconsequence of the field equations (rather than as a"compensating field" introduced to secure gaugeinvariance). There is no need for symmetry breaking toaccommodate mass, because the U(1) × SU(2) gaugesymmetry is approximate from the outset. Thegravitational field is described by the space-timemetric, as in general relativity. The electroweak fieldis described by the "mixed symmetry" part of the Riccirotation coefficients. The gauge symmetry-breakingquantity is a vector formed by contracting theLevi-Civita symbol with the totally antisymmetric partof the Ricci rotation coefficients.     

Unification of Spins and Charges

Polynomials in Grassmann algebra can be used to describe the internal degrees, spins and charges of spinors, scalars, and vectors. It was shown by Manko Bortnik and Nielsen that Kähler spinors can be generalized to describe spins of vectors as well as spins and charges of scalars, vectors, and spinors. In dimensions 14 and higher, the spontaneous breaking of symmetry leads gravity in d dimensions to manifest in 4-dimensional subspace as ordinary gravity and all needed gauge fields as well as the Yukawa couplings. Both approaches, Kähler's one (if generalized) and ours, manifest four generations of massless fermions, which are left-handed SU(2) doublets and right-handed SU(2) singlets. A possible way of spontaneously breaking symmetries is pointed out at the level of canonical momentum.     

规范作用与引力的统一

在标准模型手征扩充理论的基础上,假定规范作用与引力统一,计算表明,夸克和轻子只可能有三代;所定出的统一点的能量标度为4.4×10¹⁸GeV轻子性夸克的质量标度为10¹⁰GeV.     

Gauge and Space-Time Symmetry Unification

Unification ideas suggest an integral treatment of fermion and boson spin andgauge-group degrees of freedom. Hence, a generalized quantum field equation,based on Dirac's, is proposed and investigated which contains gauge and flavorsymmetries, determines vector gauge field and fermion solution representations,and fixes their mode of interaction. The simplest extension of the theory with a6-dimensional Clifford algebra has an SU(2) _L × U(1) symmetry, which isassociated with the isospin and the hypercharge, their vector carriers, two-flavorcharged and chargeless leptons, and scalar particles. A mass term producesbreaking of the symmetry to an electromagnetic U(1), and a Weinberg's angle_W with sin ²(_W) = 0.25. A more realistic 8D extension gives coupling constantsof the respective groups g = 1/2 .707 and g = 1/6 .408, with thesame _W.     

Unification of the forces

Unification of the forces is achieved via an elementary application of the symmetry of parity-time-charge (PTC) inversion invariance to classical physics. The strong color force between quarks is found to be a PTC-inversion of the Coulomb force and to have a strength of about 3.75×10⁵ times the Coulomb force between electrons at a separation distance equal to the electron Coulomb radius, r₀/2 0.7045×10^–13 cm [note that what we call the electron Coulomb radius (a convenient unit) differs by a factor of 4 from the usual classical electron radius]. It displays asymptotic freedom as predicted and, consistent with the predicted spatial variation, it is found to be constant, or independent of the particle separation distance. The strong color force and other PTC-inverse EM forces are found to exist only between quarks, whereas the EM forces are found to exist only between leptons and composite particles.The weak force is the residual of long range EM and PTC-inverse EM forces (a similar situation is indicated of the short-range nucleon-nucleon force). These residual forces are of mixed parity.The net potentials between particles are polynomials in the separation variable r, which have minima and maxima at the zeros of the first derivative. The minima are the stable orbits, which provides a classical basis for quantum mechanics.Finally, the Coulomb and the gravitational forces are found to be non-reciprocal P-inversions of each other and become indistinguishable at m_x = ±(2) (q_x/e)M_p, where M_p is the Planck mass.     

Unification of Quantum Theory and Relativity

A underlying dynamical structure for bothrelativity and quantum theory —superrelativity — has been proposedin order to overcome the well-known incompatibilitybetween these theories. The relationship between curvature of spacetime (gravity) andcurvature of the projective Hilbert space of purequantum states is established as well.     

Unification of Electromagnetic Interactions and Gravitational Interactions

Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper.Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same mannerand are unified in a semi-direct product group of U(1) Abelian gauge group and gravitational gauge group.     

Unification of fermion and Boson stochastic calculus

Fermion annihilation and creation processes are explicitly realised in Boson Fock space as functions of the corresponding Boson processes and second quantisations of reflections. Conversely, Boson annihilation and creation processes can be constructed from the Fermion processes. The existence of unitary stochastic evolutions driven by Fermion and gauge noise is thereby reduced to an equivalent Boson problem, which is then solved.This work was carried out while both authors were participating in the Symposium on Stochastic Differential Equations at the University of Warwick. The first author acknowledges conversations with R.F. Streater during the same Symposium     

On the Reflection and Diffraction of Hard Gamma Quanta at the Crystal Surface

The interaction between hard gamma quanta and a crystal surface is considered in the case of grazing incidence. It is shown that, under certain conditions, such interaction can be described within the framework of classical wave theory even if the particle energy exceeds 10² GeV.     

Canonical Quanta1 Symmetry and Conserved Charges for a System with Higher-Order Lagrangian

Based on the phase space generating functional of Green function for a system with regular higher-order Lagrangian, the conserved charge is deduced at quantum level if the canonical action is invariant under the global symmetry transformation in extended phase space. The generalization of our results to a system with singular higher-order Lagrangian is also studied. In general the quantal conserved charges are different from classical ones.