On colors and electric charges of quarks: modeling in terms of groups U(n) and SU(n,n)

Levichev, A. V.; Palyanov, Andrey

doi:10.24147/2222-8772.2020.4.31-40

Cited by 3 publications

(22 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should always be stated (or should be clear from the context) which U(n)-level such an rgroup is associated with. From [5], we now reproduce the following statement [5] (Theorem 4.1).…”

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 96%

“…Below (in this Section), we will give more details from [10]. In particular, in the general context of how to mathematically define the notion of an elementary particle, we will comment on the transition from the renowned Wigner method to (what have been coined in [5] as) the Wigner-Segal method. Meanwhile we only state the following (it is an extract from [10]): there is a certain (infinite-dimensional) Hilbert space Fp (of functions on the Minkowski space-time M) which is interpreted as the set of all (theoretically possible) states (or wave functions) of the chronometric proton p (see formula (20) of [10] and Theorem 3.1 of [9]).…”

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 99%

“…For each of our fermions of the level U(3), its rgroup G can be any of G12, G13, or G23. Such a convention was a mathematical basis for defining the notion of a color of an MLM-quark (see Sections 3 and 4 of [5], as well as our Section 5, below ). Clearly, each MLM-quark is as fully described, as the chronometric proton was -see our Theorem 2, from above.…”

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 99%

“…In [3] Segal treats certain representations of G = SU (2,2). This latter group (sometimes called the conformal group) contains both the (11-dimensional) extended Poincare group P + and its (10-dimensional) subgroup P. In [5] it was suggested to name the approach of [3] as the Wigner-Segal method. The abbreviation SM stands for the (currently widely accepted) Standard Model.…”

Section: Introductionmentioning

confidence: 99%

“…In [1,2] the MLM was described as an alternative to the SM. On the basis of further studies (see [5][6][7][8][9][10]), MLM can now be viewed as the symbiosis of Segal's Chronometry with SM. The main purpose of the current review is to put together concise and, hopefully, convincing arguments in order to support such a far-reaching view.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

Levichev¹,

Palyanov²

2022

Preprint

View full text Add to dashboard Cite

The Multi-Level Model (=MLM) was suggested by A. Levichev as a description of quarks and gluons. The review recalls MLM-terminology while MLM-findings (for quarks and leptons) are compared to the experimental data as accepted by the Standard Model (=SM). MLM is based on Segal’s compact space-time U(2) and on the sequence of embeddings: U(2) into U(3), U(2) into U(4), etc. These groups were called the levels (of matter): U(2) - the 0th (that is, our mundane world), U(3) - the 1st, U(4) - the 2nd, etc. Such a convention matches the SM-quarks' generations list. Each SM-quark is viewed either as a sunken proton, or as a captured proton. The MLM-proton is elementary and indestructible (hence no need for confinement). For MLM-quarks, in terms of the notion of a ruling group, flavor and color are defined mathematically. The number of colors (and of flavors) is level-dependent. For levels U(3) through U(6) the correspondence with the SM-quarks is established. Three new quarks and two new leptons are predicted. The SM-puzzle of quark and lepton generations is solved. Using the Han-Nambu scheme, the notion of the quark’s electric charge is expressed in terms of color charges. The original part of the review suggests studying the proton’s properties (like mass, shape and inner pressure) on the ba-sis of its wave function.

show abstract

“…It should always be stated (or should be clear from the context) which U(n)-level such an rgroup is associated with. From [5], we now reproduce the following statement [5] (Theorem 4.1).…”

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 96%

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 99%

Section: From Chronometry To the Mlm-quarks Of The U(3)-levelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

Levichev¹,

Palyanov²

2022

Preprint

View full text Add to dashboard Cite

show abstract

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

Levichev¹,

Palyanov²

2022

Preprint

View full text Add to dashboard Cite

The Multi-Level Model (=MLM) was suggested by A. Levichev as a description of quarks and gluons. The review recalls MLM-terminology while MLM-findings (for quarks and leptons) are compared to the theoretical and experimental data as accepted by the Standard Model (=SM). MLM is based on Segal’s compact space-time U(2) and on the sequence of embeddings: U(2) into U(3), U(2) into U(4), etc. These groups were called the levels (of matter): U(2) - the 0th (that is, our mundane world), U(3) - the 1st, U(4) - the 2nd, etc. Such a convention matches the SM-quarks' generations list. Each SM-quark is viewed either as a sunken proton, or as a captured proton. The MLM-proton is elementary and indestructible (hence no need for confinement). For MLM-quarks, in terms of the notion of a ruling group, flavor and color are defined mathematically. The number of colors (and of flavors) is level-dependent. For levels U(3) through U(6) the correspondence with the SM-quarks is established. Three new quarks and two new leptons are predicted. The SM-puzzle of quark and lepton generations is solved. Using the Han-Nambu scheme, the notion of the quark’s electric charge is expressed in terms of color charges. The original part of the review suggests studying the proton’s properties (like mass, shape and inner pressure) on the ba-sis of its wave function.

show abstract

Perspective Chapter: The Proton’s Theoretical Description, Based on Wigner-Segal Approach to Elementary Particles

Klevtsova,

Levichev,

Neshchadim

et al. 2023

Proton Therapy - Scientific Questions and Future Direction

View full text Add to dashboard Cite

The chapter focuses on the Multi-Level Model (MLM), a conceptual framework proposed by Levichev. The essence of the MLM is the amalgamation of Segal’s chronometry and the Standard Model (SM), a fundamental theory in particle physics. The potential applications of MLM in proton therapy are predicated on the concept of the infinite-dimensional space denoted as Fp, encompassing the entirety of proton wave functions. The inherent properties of Fp-elements f are outlined. This analysis then proceeds to capture distinct instances (“snap shot photos”) of these functions at the temporal instant t = 0. The corresponding graphical representations of these functions are elucidated using precise geometric terminology. Specifically, two distinct types of graphs are identified: ND) a bell-shaped surface lacking a central depression, and WD) a bell-shaped surface featuring a central dent. In an endeavor to establish a connection between these mathematical revelations and proton therapy dosimetry, the exploration delves into a comparison of various classes of functions f from Fp with those produced within diverse proton therapy vaults. This integration proposes the incorporation of a novel ingredient into dosimetry, namely, the incorporation of the proton’s wave function. This innovative approach holds promise for refining proton therapy techniques and enhancing treatment precision.

show abstract

On colors and electric charges of quarks: modeling in terms of groups U(n) and SU(n,n)

Cited by 3 publications

References 3 publications

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

The Multi-Level Model for Quarks and Leptons as the Symbiosis of Segal’s Chronometry with the Standard Model

Perspective Chapter: The Proton’s Theoretical Description, Based on Wigner-Segal Approach to Elementary Particles

Contact Info

Product

Resources

About