Intrinsic Quantum Mechanics. Particle physics applications on U(3) and U(2) (original) (raw)

Intrinsic quantum mechanics behind the Standard Model?

Proceedings of European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2019)

We suggest the gauge groups SU(3), SU(2) and U(1) to share a common origin in U(3). We take the Lie group U(3) to serve as an intrinsic configuration space for baryons. A spontaneous symmetry break in the baryonic state selects a U(2) subgroup for the Higgs mechanism. The Higgs field enters the symmetry break to relate the strong and electroweak energy scales by exchange of one quantum of action between the two sectors. This shapes the Higgs potential to fourth order. Recently intrinsic quantum mechanics has given a suggestion for the Cabibbo angle from theory (EPL124-2018) and a prediction for the Higgs couplings to gauge bosons (EPL125-2019). Previously it has given the nucleon mass and the parton distribution functions for u and d quarks in the proton (EPL102-2013). It has given a quite accurate equation for the Higgs mass in closed form (IJMPA30-2015) and an N and Delta spectrum essentially without missing resonances (arXiv:1109.4732). The intrinsic space is to be distinguished from an interior space. The intrinsic space is non-spatial, i.e. no gravity in intrinsic space. The configuration variable is like a generalized spin variable excited from laboratory space by kinematic generators: momentum, spin and Laplace-Runge-Lenz operators. The baryon dynamics resides in a Hamiltonian on U(3) and projects to laboratory space by the momentum form of the wavefunction. The momentum form generates conjugate quark and gluon fields. Local gauge invariance in laboratory space follows from unitarity of the configuration variable and left invariance of the coordinate fields on the intrinsic space. Future work should aim to invoke leptons in the second and third generations and quarks in the third.

On quarks and the origin of QCD: Partons and baryons from intrinsic states

Europhysics Letters, 2021

We create quarks from baryons in stead of constituting baryons from quarks. The quantum fields of QCD are generated via the exterior derivative (momentum form) of baryon wave functions on an intrinsic configuration space, the Lie group U(3). Local gauge transformations correspond to coordinate translations in the intrinsic space. A proton spin structure function and a proton magnetic moment are derived. We show how the spectrum of unflavoured baryons, the N and Delta resonances, can be understood from a mass Hamiltonian on the intrinsic space and note how our model resolves the problem of colour confinement. We calculate an approximate value for the relative neutron-to-proton mass shift and give an exact value for the neutron mass. We predict neutral charge singlets that may be interpreted as neutral pentaquarks at LHCb.

Towards solving the proton spin puzzle

2019

The fact that the spins of the quarks in the proton, as measured in deep inelastic lepton scattering, only add up to about 30% of the spin of the proton is still not understood after 30 years. We show that our newly developed model for the quark and gluon momentum distributions in the proton, based on quantum fluctuations of the proton into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons, can essentially reproduce the data on the proton spin structure function g_1^P(x) and the associated spin asymmetry. A further improved description of the data is achieved by also including the relativistic correction of the Melosh transformation to the light-front formalism used in deep inelastic scattering. However, this does not fully resolve the spin puzzle, including also the neutron spin structure and the spin sum rules. These aspects can also be accounted for by our few-parameter model if the conventional SU(6) flavor-spin symmetry is broken, giving n...

Gauge Theory in Elementary Particle Physics: A Comprehensive Overview

RG, 2024

Gauge theory has revolutionized our understanding of elementary particles and their interactions. This research paper explores the principles and applications of gauge theory in particle physics, focusing on its development, theoretical framework, and experimental confirmations. We delve into the fundamental forces, gauge invariance, and the significance of the Standard Model. Additionally, we examine recent advancements and ongoing research in the field.

Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions

Physical Review D, 1973

An attempt is made to unify the fundamental hadrons and leptons into a common irreducible representation I of the same symmetry group G and to generate a gauge theory of strong, electromagnetic, and weak interactions. Based on certain constraints from the hadronic side, it is proposed that the group 6 is SU(4') x SU(4"), which contains a Han-Nambu-type SU(3') x SU{3")group for the hadronic symmetry, and that the representation I' is (4, 4*). There exist four possible choices for the lepton number L and accordingly four possible assignments of the hadrons and leptons within the (4, 4*). Two of these require nine Han-Nambu-type quarks, three "charmed" quarks, and the observed quartet of leptons. The other two also require the nine Han-Nambu quarks, plus heavy leptons in addition to observed leptons and only one or no "charmed" quark. One of the above four assignments is found to be suitable to generate a gauge theory of the weak, electromagnetic, and SU(3") gluonlike strong interactions from a selection of the gauges permitted by the model. The resulting gauge symmetry is SU(2')z x U(1) x SU(3")z,+z. The scheme of all three interactions is found to be free from Adler-Bell-Jackiw anomalies. The normal strong interactions arise effectively as a consequence of the strong gauges SU{3")z, z. Masses for the gauge bosons and fermions are generated suitably by a set of 14 complex Higgs fields. The neutral neutrino and AS =0 hadron currents have essentially the same strength in the present model as in other SU(2)L, x U(1) theories. The mixing of strongand weak-gauge bosons (a necessary feature of the model) leads to parity-violating nonleptonic amplitudes, which may be observable depending upon the strength of SU(3") symmetry breaking. The familiar hadron symmetries such as SU{3') and chiral SU(3')& xSU(3')z are broken only by quark mass terms and by the electromagnetic and weak interactions, not by the strong interactions. The difficulties associated with generating gauge interactions in the remaining three assignments are discussed in Appendix A. Certain remarks are made on the question of proton and quark stability in these three schemes,

A Simple Introduction to Particle Physics I: Foundations and the Standard Model

This is the first of a series of papers in which we present a brief introduction to the relevant mathematical and physical ideas that form the foundation of Particle Physics, including Group Theory, Relativistic Quantum Mechanics, Quantum Field Theory and Interactions, Abelian and Non-Abelian Gauge Theory, and the SU(3)xSU(2)xU(1) Gauge Theory that describes our universe apart from gravity. These notes are not intended to be a comprehensive introduction to any of the ideas contained in them. Among the glaring omissions are CPT theorems, evaluations of Feynman Diagrams, Renormalization, and Anomalies. The topics were chosen according to the authors preferences and agenda. These notes are intended for a student who has completed the standard undergraduate physics and mathematics courses. Furthermore, these notes should not and will not in any way take the place of the related courses, but rather provide a primer for detailed courses in QFT, Gauge Theory, String Theory, etc., which will fill in the many gaps left by this paper.

A Higgs at 125 GeV and baryon mass spectra derived from a common U(3) framework

Proceedings of The European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2015), 2016

Baryons are described by a Hamiltonian on an intrinsic U(3) Lie group configuration space with electroweak degrees of freedom originating in specific Bloch wave factors. By opening the Bloch degrees of freedom pairwise via a U(2) Higgs mechanism, the strong and electroweak energy scales become related to yield the Higgs mass 125.085+/-0.017 GeV and the usual gauge boson masses. From the same Hamiltonian we derive both the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict neutral flavour baryon singlets to be sought for in negative pions scattering on protons or in photoproduction on neutrons and in invariant mass like Σ + c (2455)D − from various decays above the open charm threshold, e.g. at 4499, 4652 and 4723 MeV. The fundamental predictions are based on just one length scale and the fine structure coupling. The interpretation is to consider baryons as entire entities kinematically excited from laboratory space by three impact momentum generators, three rotation generators and three Runge-Lenz generators to internalize as nine degrees of freedom covering colour, spin and flavour. Quark and gluon fields come about when the intrinsic structure is projected back into laboratory space depending on which exterior derivative one is taking. With such derivatives on the measurescaled wavefunction, we derived approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.

Extended Particle Model of Leptons and Quarks and Generalized Kaluza's Unified Field Theory

Progress of Theoretical Physics Supplement, 1979

As a unified model of leptons and quarks, a relativistic deformable rotator model is investigated. It gives a substantial interpretation to the Weinberg-Salam theory and brings several characteristic results: i) Intrinsic spin and weak-isospin of leptons and quarks are mutually inseparabfe quantities related to the rotational mode of the rotator, and each must have the SU2 structure. ii) There arise newly SU, X SU, freedoms from the rotational mode of the principal axes of deformation of the rotator, which are assigned to two kinds of new flavor isospins, L and M. iii) Further, from the dilatation mode in the direction of each principal axis of deformation, the freedom of U, is derived, and identified with the colour SU,' and the quantum number which discriminates between leptons and quarks. iv) For the consistent description of this kind of extended particles, it becomes necessary to introduce the framework of the (4+n)-dimensional space of the generalized Kaluza's unified field theory, whose metric tensor r.tB(A, B=1,2, .. •,4+n) naturally provides Yang-Mills fields A,"(a=l, 2, ... , n) needed to localize internal symmetries of the extended particles, and scalar fields Yab(a,b=l, 2, ... , n) identified with Higgs mesons, in addition to the gravitational tensor g,,. v) It predicts the existence of the fourth sequential doublets of leptons and quarks subsequent to (v., t') and (t, b), together with possible more complicated excited-states of leptons and quarks. Contents Generally covariant wave equation of the basic matter Elimination of ea-dependence of basic fields Gauge transformation as the special coordinate transformation Concluding remarks and further outlook