The Complex Field Theory and Mass Formation—An Alternative Model to Higgs Mechanism

The electromagnetic force, strong nuclear force, weak nuclear force, and gravitational force are the four fundamental forces of nature. The Standard Model (SM) succeeded in combining the first three forces to describe the most basic building blocks of matter and govern the universe. Despite the model’s great success in resolving many issues in particle physics but still has several setbacks and limitations. The model failed to incorporate the fourth force of gravity. It infers that all fermions and bosons are massless contrary to experimental facts. In addition, the model addresses neither the 95% of the universe’s energy of Dark Matter (DM) and Dark Energy (DE) nor the universe’s expansion. The Complex Field Theory (CFT) identifies DM and DE as complex fields of complex masses and charges that encompasses the whole universe, and pervade all matter. This presumption resolves the issue of failing to detect DM and DE for the last five decades. The theory also presents a model for the universe’s expansion and presumes that every material object carries a fraction of this complex field proportional to its mass. These premises clearly explain the physical nature of the gravitational force and its complex field and pave the way for gravity into the SM. On the other hand, to solve the issue of massless bosons and fermions in the SM, Higgs mechanism introduces a pure and abstractive theoretical model of unimaginable four potentials to generate fictitious bosons as mass donors to fermions and W± and Z bosons. The CFT in this paper introduces, for the first time, a physical explanation to the mystery of the mass formation of particles rather than Higgs’ pure mathematical derivations. The analyses lead to uncovering the mystery of electron-positron production near heavy nuclei and never in a vacuum. In addition, it puts a constraint on Einstein’s mass-energy equation that energy can never be converted to mass without the presence of dense dark matter and cannot be true in a vacuum. Furthermore, CFT provides different perspectives and resolves real-world physics concepts such as the nuclear force, Casimir force, Lamb’s shift, and the anomalous magnetic moment to be published elsewhere.

Higgs-Like Mechanism by Confinement of Quarks in a Chemical Non-Equilibrium Model

A chemical non-equilibrium equation for binding of massless quarks to antiquarks, combined with the spatial correlations occurring in the condensation process, yields a density dependent form of the double-well potential in the electroweak theory. The Higgs boson acquires mass, valence quarks emerge and antiparticles become suppressed when the system relaxes and symmetry breaks down. The hitherto unknown dimensionless coupling parameter to the superconductor-like potential becomes a re-gulator of the quark-antiquark asymmetry. Only a small amount of quarks become “visible”—the valence quarks, which are 13% of the total sum of all quarks and antiquarks—suggesting that the quarks-antiquark pair components of the becoming quark-antiquark sea play the role of dark matter. When quark-masses are in-weighted, this number approaches the observed ratio between ordinary matter and the sum of ordinary and dark matter. The model also provides a chemical non-equilibrium explanation for the information loss in black holes, such as of baryon number.

Mass-Oscillators as Information Memories of Action

In the theory of physical information, the physical phenomena of electromagnetism, quantum mechanics and gravity can be described by means of the action as information enclosed in four dimensional structures with oscillator properties, under the conditions of the Hamilton principle. The present report shows that it is also possible to simulate the behaviour of the mass under these conditions. As a result, among other things, the statements are obtained that the mass is stored virtual action;the rest frame of elementary objects and the inertia of matter are caused by the action stored in the mass oscillators.

E. Cartan’s and A. Connnes’ Supersymmetry and Differences of Understanding Physical Phenomena

Einstein claimed that one cannot de？ne global time, and proposed de？ning local time additionally. Such approach was adopted also by E. Cartan, in which fermions are described by spinors with 16 bases and interact with vectors with 8 bases, that consists of a couple of 4 dimensional vectors xi （i = 1, …, 4） and xi （i = 1, …,4）. In Cartan’s theory, spinors and vectors transform by super symmetric transformations G23, G12, G13, G123 and G132 and bases of fermion spinors consist of ξ0,ξi （i = 1, ···, 4）, ξ1234, ξ234, ξ134, ξ124, ξ123 and ξi,j （i /= j ∈{1,2,3,4}）. Except G23, the transformations mix spinors and vectors, and operations of G23 on spinors contain G23 ξ4 = ξ0 and G23 ξ123 = ξ1234, and operations of G23 on vectors contain G23x4 = ？x4＇ and G23 x4＇= ？x4. Therefore, there are 14 independent spinor bases and 7 independent vector bases, which corresponds to the number of bases of the G2 symmetry. From the bases of non-commutative geometry, Connes took two ？bers from a point of S3 basis, and on top of ？bers allowed two times propagate following von Neumann algebra, but evolution of the system was assumed to be de？ned by one-parameter group of transformation.Steenrod stated that the S7 symmetry can be regarded as S3 symmetry covered over S4 symmetry, which allows decomposition of S7 × R8 → （S3 × R4） × （S3 × R4）. We assume there is a space-time representation by an algebra C（V） of smooth function and matrix algebra Mnand transformations A are expressed as A = C（V ） Mn. In order to make total momentum space to remain 4 dimensional, the group of A becomes SO（3 ＋ n^2 -1,1）-SO（3,1） × SOn^2-1 in Minkowski space. We choose n = 3 and construct SO8 on R8 ？ R4,4. We apply this model to understanding experimentally observed CP violation in pp→ tt or bb and in pp → （H →bb） ＋ ll ＋jets and Time Reversal Based Nonlinear Elastic Wave Spectroscopy （TR-NEWS） method.

E. Cartan’s Supersymmetry,Noncommutative Geometry and Propagation of Time in S7 × R^4 Spacetime

Einstein claimed that one cannot de？ne global time, and in order to formulate physical dynamics, it is useful to adopt ？ber bundle structure. We de？ne topological space E which consists of base space X and ？bers F = Π-1（X）, where Π is a projection of an event on the base space. Relations between initial data and ？nal data are de？ned by group G and a Fiber bundle is de？ned as as set （E, Π, F, G, X）.Tangent bundle TX of real linear space X is de？ned by the projection πTX = TX → X; （x,a） → a for any a ∈ X and a sphere Sn any non negative integer n may be thought to be a smooth submanifold of Rn＋1 and TSn is identi？ed as {（x,a） ∈Rn＋1 ×Sn ： x·a = 0} Connes proposed that when one adopts non-commutative geometry, one can put two ？bers at each point of X and on top of the two ？bers de？ne the initial input event and the ？nal detection event. When one considers dynamics of leptons de？ned by Dirac equation, group G is given by quaternions H, and the base space X is usually taken to be S3. E. Cartan studied dynamics of spinors which are described by octonions or Cayley numbers which is an ordered product of two quaternions. The asymptotic form Y of this system is S7. Cayley numbers of S7 are de？ned as a 3-sphere bundle over S4 with group S3. Therefore in T X there are two manifolds S3 × R4 and S3＇ × R4 and the direction of propagation of time on S3 and S＇3 are not necessarily same. We apply this formulation to experimentally observed violation of time reversal symmetry in pp→ tt process and for understanding the result of time reversal based nonlinear elastic wave spectroscopy （TR-NEWS） in memoducers.