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Register a new userLorentz group and mass spectrum of elementary particles
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V.V. Varlamov
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Mass spectrum of localized states (elementary particles) of single quantum system is studied in the framework of Heisenbergs scheme. Localized states are understood as cyclic representations of a group of fundamental symmetry (Lorentz group) within a Gelfand-Neumark-Segal construction. It is shown that state masses of lepton (except the neutrino) and hadron sectors of matter spectrum are proportional to the rest mass of electron with an accuracy of $0,41%$.
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We extend the quantum-mechanical results of Muller & Saunders (2008) establishing the weak discernibility of an arbitrary number of similar fermions in finite-dimensional Hilbert-spaces in two ways: (a) from fermions to bosons for all finite-dimensional Hilbert-spaces; and (b) from finite-dimensional to infinite-dimensional Hilbert-spaces for all elementary particles. In both cases this is performed using operators whose physical significance is beyond doubt.This confutes the currently dominant view that (A) the quantum-mechanical description of similar particles conflicts with Leibnizs Principle of the Identity of Indiscernibles (PII); and that (B) the only way to save PII is by adopting some pre-Kantian metaphysical notion such as Scotusian haecceittas or Adamsian primitive thisness. We take sides with Muller & Saunders (2008) against this currently dominant view, which has been expounded and defended by, among others, Schrodinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Mittelstaedt, Giuntini, Castellani, Krause and Huggett.
From the observed results, we deduced that the mass of the neutrino is about 10^(-1) eV and the mass of the fourth stable elementary particle (delta) is about 10^(0) eV. While neutrino is related to electro-weak field, the fourth stable elementary particle delta is related to gravitation-strong field, and some new meta-stable baryons may appear near the TeV region. Therefore, a twofold standard model diagram is proposed, and involves some experiment phenomena: The new meta-stable baryons decays produce delta particles, which are helpful in explaining the Dijet asymmetry phenomena at LHC of CERN, the different results for the Fermilabs data peak, etc; However, according to the (B-L) invariance, the sterile neutrino about the event excess in MiniBooNe is not the fourth neutrino but rather the delta particle; We think that the delta particles are related to the phenomenon about neutrinos FTL, and that anti-neutrinos are faster than neutrinos. FTL is also related to cosmic inflation, singular point disappearance, a finite universe, and abnormal red shift of SN Ia. Besides, the dark matter particles with low mass are helpful in explaining missing solar neutrinos, the CMB angular power spectrum measured by WMAP etc. Some experiments and observations are suggested, especially about the measurement for the speed of gravitational wave c. c and c, in physics, represent the limit speeds of moving particles made by different categories of matter with different Lorentz factors. Lorentz transformation is compatible with FTL. This will be helpful to look for new particles.
On the basis of the three fundamental principles of (i) Poincar{e} symmetry of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector particles, i.e., massive spin-1 particles transforming in the /1/2,1/2) representation space of the Homogeneous Lorentz Group (HLG). We make the point that the first two symmetries alone do not fix the electromagnetic couplings uniquely but solely prescribe a general Lagrangian depending on two free parameters, here denoted by xi and g. The first one defines the electric-dipole and the magnetic-quadrupole moments of the vector particle, while the second determines its magnetic-dipole and electric-quadrupole moments. In order to fix the parameters one needs an additional physical input suited for the implementation of the third principle. As such, one chooses Compton scattering off a vector target and requires the cross section to respect the unitarity bounds in the high energy limit. In result, we obtain the universal g=2, and xi=0 values which completely characterize the electromagnetic couplings of the considered elementary vector field at tree level. The nature of this vector particle, Abelian versus non-Abelian, does not affect this structure. Merely, a partition of the g=2 value into non-Abelian, g_{na}, and Abelian, g_{a}=2-g_{na}, contributions occurs for non-Abelian fields with the size of g_{na} being determined by the specific non-Abelian group appearing in the theory of interest, be it the Standard Model or any other theory.
In this article the concept of mass is analyzed based on the special and general relativity theories and particle (quantum) physics. The mass of a particle (m=E(0)/c^2) is determined by the minimum (rest) energy to create that particle which is invariant under Lorentz transformations. The mass of a bound particle in the any field is described by m<E80)/c^2 and for free particles in the non-relativistic case the relation m=E/c^2 is valid. This relation is not correct in general, and it is wrong to apply it to the radiation and fields. In atoms or nuclei (i.e. if the energies are quantized) the mass of the particles changes discretely. In non-relativistic cases, mass can be considered as a measure of gravitation and inertia.
Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin particles, this equation is reduced to the sets of two-component independent matrix equations. It is shown that the relativistic scalar and integral spin particles are described by component equation.
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