This work analyzes the mathematical coherence of the electroweak theory.Quantum electrodynamics proves that the Dirac electron quantum function ψ has four degrees of freedom.This theory has solid experimental support.Furthermore, the rank of the matrix ( ) 5 1 γ ± is 2. Therefore, the electroweak theory that uses the product of this matrix and the Dirac electron function: ( ) 5 1 weak ψ γ ψ = ± has a mathematically erroneous structure because weak ψ assigns only two degrees of freedom to the function of the same elec-tron.An independent analysis supports this assertion because it shows a different argument that refutes the mathematical structure of the electroweak theory.

The distinction between the concepts of a Necessary Condition and a Sufficient Condition is a fundamental element of mathematics.This issue certainly applies to physics which has a mathematical structure.However, this work shows that sometimes physical textbooks ignore this distinction.An analysis of the conserved 4-current of the Noether theorem proves that this issue is extremely important.The analysis uses the dimension of the Lagrangian density and the corresponding dimension of the quantum function of physical theories.It is proved that the QED theory of a Dirac electron yields a coherent expression for the 4-current and the QED interaction term.In construct, the Klein-Gordon theory of a charged particle as well as the electroweak theory of the W ± particles violates Maxwellian electrodynamics.Unlike the Dirac electron, these theories have no coherent interaction term between the 4-current of the charged particle and the electromagnetic fields.This result relies on new necessary conditions that are required for the compatibility of the 4-current of a charged quantum particle.The new necessary conditions prove that the continuity equation of the Noether theorem is not a sufficient condition for an acceptable 4-current.

The study of the diet of Bagrus bajad (Bagridae) was carried out on 520 specimens from the south-west of Lake Albert from December 2019 to December 2020.The relative importance index of food was used to evaluate quantitative aspect of diet.Percentages of global vacuity and average intestinal coefficient were 23.40% and 1.35, respectively.Analysis of 418 food-containing stomachs revealed that this fish has an omnivorous diet predominated by piscivorous and insectivorous.Larvae and juvenile fish of Haplochromis spp and Oreochromis spp and insects are the main foods.Molluscs, plant debris, plankton, etc. are accessory foods.Comparison between specimens of different sizes showed no variation in diet.On other hand, a significant difference was noted in the food between sexes according to hydrological seasons.This difference reflects an abundance of food resources in rainy season which reduces food competition.Good fishing regulations should be established taking into account the seasons and the conservation of habitats that abound in the different types of food consumed by B. bajad.

The concept of density in quantum theories of an elementary particle is discussed.Density is, at least implicitly, recognized in contemporary textbooks on quantum field theories, where the Noether theorem is utilized for a derivation of a conserved 4-current , 0 j µ µ = and a conserved energy-momentum tensor , 0 T µν ν = .Here the component 0 j is the particle's density and the compo- nents 0 T µ are the energy-momentum density.The novelty of this work is the analysis of the particle's density and the energy-momentum density of these expressions and their application to several specific quantum theories.As of today, these tasks have not been adequately accomplished in contemporary textbooks.The results show that the first-order Dirac theory of an elementary massive spin-1/2 particle yields consistent results.In contrast, secondorder quantum theories, such as the Klein-Gordon theory, the electroweak theory of the , W Z ± particles, and the Higgs boson theory are inherently wrong.

The significance of the interaction term of classical electrodynamics and quantum electrodynamics is analyzed.It is proven that this term is involved in the derivation of the equations of motion of the charge-carrying particles and the Maxwell equations of the electromagnetic fields.Classical electrodynamics, as well as quantum electrodynamics of Maxwell equations and the Dirac equation of a charged spin-1/2 particle, comply with the dual role of the interaction term.Inconsistencies arise from the equations of the Klein-Gordon particles, the electroweak theory of the W ± , and the Proca theory of a massive photon.The experimental data and the incoherent structure of the mainstream literature substantiate these results.

The paper emphasizes the significance of density of an elementary massive quantum particle.In quantum field theory, a quantum function of an elementary particle takes the form of ( ) ,t ψ r .This kind of function is used for putting the inner product of the corresponding Hilbert space in the form of an appropriate integral, and the inner product of a function with itself depends on the particle's density.Density also affects the multi-particle Fock space, because this space relies on single-particle Hilbert space.This work shows a new reason where a coherent theoretical expression for the density of an elementary particle is required: A theoretical description of experiments that measure the transition of unstable states and the decay of an elementary quantum particle.This new aspect of density strengthens its meaning in quantum theories.The usefulness of this outcome is shown in its application to the decay of the muon and the electroweak's , W Z ± particles.It turns out that the Dirac theory provides a consistent description of the muon decay.In contrast, the electroweak theory fails to explain the decay of the , W Z ± particles.

The foundations of the mathematical structure of quantum theories of a massive particle are the basis of this analysis.It proves the coherence of the particle-wave duality of quantum theories and the principle of complementarity as well.Furthermore, the noncommutativity of Hermitian operators proves that quantum theories are inherently indeterministic.This feature does not deny the fact that the classical limit of quantum theories agrees with classical physics.It is also shown that the foundations of the mathematical structure of quantum theories impose constraints on any specific quantum theory.It is proved that the first-order Dirac theory is consistent with all constraints.In contrast, second-order theories, such as the Klein-Gordon, the electroweak theory of the W ± and the Z particles, and the Higgs boson theory fail to do that.An analogous analysis proves that also the Majorana neutrino theory is inconsistent with fundamental requirements.Similarly, inconsistencies of Proca's idea about a massive photon are shown.

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

It is now recognized that a neutrino is a massive spin-1/2 particle. Consequently, neutrino- antineutrino pair production and their pair annihilation are theoretically valid processes. The data prove that the strength of weak interactions increases with collision energy. Therefore, a neutrino pair production event is expected to be a significant process in the region which is just outside the event horizon of a black hole. Another neutrino source is the pair production of particles like muons and charged pions whose decay produces neutrinos. Similarly, copious neutrino pair production events are expected to take place right after the big bang. Since a neutrino does not directly participate in electromagnetic interactions, its pair annihilation cannot directly produce photons. For this reason, a low energy neutrino-antineutrino collision can only go to another neutrino-antineutrino pair. It follows that the number of low energy neutrinos increases with time. This effect may contribute to the problem of the missing mass of the universe.

The compatibility of the strong interaction theory called Quantum Chromodynamics (QCD) with relevant experimental data is critically examined. The clear advantage of the Regular ChargeMonopole Theory over QCD is explained. An analysis of new data provides further support for this claim. The paper points out several specific effects that illustrate this conclusion: the hard photon-nucleon interaction, the striking difference between the high energy electron-proton and proton-proton cross section, the peripheral location of the proton’s antiquark, the strong CP problem, the quite large amount of the ss ¯ pair in the proton, the excess of the proton’s d¯antiquarks over its u¯ antiquarks, and the spin-dependence of high energy polarized proton-proton scattering. These problematic issues are in accordance with M. Gell-Mann’s recently published qualms about the QCD merits.

Relativistic properties of a Lagrangian density are compared with those of a Hamiltonian density.It is proved that a Lagrangian density and a Hamiltonian density undergo different Lorentz transformations.This outcome is a theoretical element that has been unnoticed for a very long time.It is also proved that this theoretical element plays a crucial role in the structure of weak interactions theory.In particular, it is shown that the theory that uses this element is overwhelmingly superior over the Standard Model electroweak theory.

The paper examines the Dirac-Pauli differences concerning the order of the primary differential equation of an elementary massive quantum particle.The analysis relies on several self-evident constraints that an acceptable quantum theory must satisfy, like conservation laws, compatibility with Maxwellian electrodynamics and the correspondence principle.The dimension of the quantum function that is used in the Lagrangian density of a given quantum theory together with the corresponding differential equations play an important role in the reasoning procedure.The paper proves that Dirac was right and that second-order quantum theories like the Klein-Gordon equation and the electroweak theory of the W ± bosons do not satisfy fundamental constraints.This outcome is inconsistent with the Standard Model of Particle Physics.

Relativistic properties of a Dirac Lagrangian density are compared with those of a Dirac Hamiltonian density. Differences stem from the fact that a Lagrangian density is a Lorentz scalar, whereas a Hamiltonian density is a 00-component of a second rank tensor, called the energy-momentum tensor. This distinction affects the form of an interaction term of a Dirac particle. In particular, a tensor interaction term of a Dirac Lagrangian density transforms to a difference between a vector and an axial vector of the corresponding Hamiltonian density. This outcome shows that fundamental principles can prove the V-A attribute of weak interactions. A further analysis supports these results. Inherent problems of the electroweak theory are discussed.

This work discusses the problem of the apparently non-symmetric form of the electromagnetic fields’ energy-momentum tensor, which is obtained from the variational principle. The analysis treats differently radiation fields and bound fields. This distinction has a solid experimental basis where the hydrogen atom proves that radiation fields and bound fields have a different spin and a different parity. A direct calculation proves that in the case of radiation fields, the variational principle yields the well known symmetric energy momentum tensor and the problem does not exist.

The Lienard-Wiechert 4-potential depends on local coordinates and on re-tarded coordinates of a charge at the source. Therefore, the 4-potential of incoming radiation fields (namely, a photon) cannot be written as a 4-vector which satisfies the locality requirement of fields of a Lagrangian density. This unsolvable problem is the underlying reason for the extremely unusual phenomenon where respectable textbooks make contradictory statements concerning whether the electromagnetic 4-potential is a 4-vector. Moreover, an analysis of well-established experimental data proves that radiation fields and bound fields are inherently different physical objects. These results indicate that the present form of quantum electrodynamics should be revised. It is further proved that in both cases the 4-potential is not a fundamental element of electrodynamics but an auxiliary quantity. For this reason, there are problems with some specific theoretical ideas that pertain to the 4-potential, like gauge transformations, the Dirac monopole theory and the Aharonov-Bohm effects.

This work analyzes quantum fields that describe particles and quantum fields that mediate interaction between particles.Criteria for the acceptability of a quantum theory are explained and used.The main result states that no genuine particle mediates interaction between other particles.It is proved that Maxwellian radiation fields, namely photons, interact with electric charges but no genuine photon is involved in a bound state of atomic electrons or in the case where an electronic beam is scattered by an electrically charged target.The term virtual photons, which describes interaction mediating electromagnetic fields, indicates that the current literature implicitly agrees with this conclusion.Analogous results are obtained for the strong nuclear force, for the strong interactions and for the weak interactions.

This work analyzes quantum fields that describe particles and quantum fields that mediate interaction between particles. Criteria for the acceptability of a quantum theory are explained and used. The main result states that no genuine particle mediates interaction between other particles. It is proved that Maxwellian radiation fields, namely photons, interact with electric charges but no genuine photon is involved in a bound state of atomic electrons or in the case where an electronic beam is scattered by an electrically charged target. The term virtual photons, which describes interaction mediating electromagnetic fields, indicates that the current literature implicitly agrees with this conclusion. Analogous results are obtained for the strong nuclear force, for the strong interactions and for the weak interactions.

The laws of Maxwellian electrodynamics are used in an analysis of the structure of the 4-potential of radiation fields. The paper examines multi-particle and single-particle effects of a radiating source. Causality of electromagnetic processes is an important element of the analysis. Covariance properties of the relevant variables are examined and the apparent non-covariance of the radiation 4-potential where A(0) equivalent to 0 in all frames is explained. It turns out that the origin of this feature stems from the multi-charge properties of radiation. It is also shown how in every Lorentz frame one can use covariant properties of radiation fields and reconstruct an appropriate 4-potential.

The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.