The root structure of the subalgebras of the group algebra of a conformal
group in the framework ... more The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
The structure of the group algebra of a conformal group (the group underlying the group-theoretic... more The structure of the group algebra of a conformal group (the group underlying the group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
The root structure of the subalgebras of the group algebra of a conformal group in the framework ... more The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan–Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
The structure of the group algebra of a conformal group (the group underlying the
group-theoretic... more The structure of the group algebra of a conformal group (the group underlying the group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
What are space and time? What do elementary particles and elements of the periodic table have in ... more What are space and time? What do elementary particles and elements of the periodic table have in common? Keywords: holism, reductionism, hylomorphism, spinors, elementary length, symmetries, long-range action
Аннотация. Что такое пространство и время? Что объединяет элементарные частицы и элементы таблицы... more Аннотация. Что такое пространство и время? Что объединяет элементарные частицы и элементы таблицы Менделеева? Сколько можно делить материю на все меньшие части и почему невозможно верифицировать теорию струн и модель кварков? Эти и другие столь же интригующие вопросы обсуждаются в предлагаемом вниманию читателей интервью с профессором СибГИУ Вадимом Варламовым.
The questions of interpretation of the algebraic formulation of a quantum theory with a binary st... more The questions of interpretation of the algebraic formulation of a quantum theory with a binary structure are considered. The possibility of constructing a quantum theory without using any classical analogies and visual images and mechanical models associated with these analogies is discussed. It is shown that the inconsistency of the quark model, as well as the Bohr model in the theory of the atom, is a consequence of the introduction of classical space-time representations to the subatomic (hadron) level.
We consider a structure of the K-Hilbert space, where K ≃ R is a field of real numbers, K ≃ C is ... more We consider a structure of the K-Hilbert space, where K ≃ R is a field of real numbers, K ≃ C is a field of complex numbers, K ≃ H is a quaternion algebra, within the framework of division rings of Clifford algebras. The K-Hilbert space is generated by the Gelfand-Naimark-Segal construction, while the generating C *-algebra consists of the energy operator H and the generators of the group SU(2, 2) attached to H. The cyclic vectors of the K-Hilbert space corresponding to the tensor products of quaternionic algebras define the pure separable states of the operator algebra. Depending on the division ring K, all states of the operator algebra are divided into three classes: 1) charged states with K ≃ C; 2) neutral states with K ≃ H; 3) truly neutral states with K ≃ R. For pure separable states that define the fermionic and bosonic states of the energy spectrum, the fusion, doubling (complexification) and annihilation operations are determined.
The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional ... more The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional reductional and alternative holistic frameworks. From the holistic viewpoint, substance (the same as energy) is the primary concept and particles are secondary and emergent. An axiomatic system is proposed where the basic notion of the spectrum of matter is defined, and the particle spectrum emerges as a result of the energy/mass quantization. A new mass formula is derived in terms of the quantum numbers related to the Lorentz group Casimir eigenvalues. It is shown that the masses of states in the lepton and hadron sectors of the spectrum of matter are proportional to the electron rest mass (quantum of mass) with an accuracy of 0, 41% on average.
The problem of the mass spectrum of elementary particles is considered from the positions of redu... more The problem of the mass spectrum of elementary particles is considered from the positions of reductionism and holism. It is shown that in the holistic description, the concept of substance (energy) is of paramount importance, and elementary particles are understood as emergent states that play a secondary role. A system of axioms is given that defines the basic definitions of the spectrum of matter. In this case, the spectrum of states ("elementary particles") appears as a result of mass (energy) quantization. A mass formula is derived that depends on the quantum numbers defining the eigenvalues of the Casimir operators of the Lorentz group.
Аннотация. Рассматривается проблема спектра масс элементарных частиц с позиций редукционизма и хо... more Аннотация. Рассматривается проблема спектра масс элементарных частиц с позиций редукционизма и холизма. Показывается, что при холистическом описании первостепенное значение приобретает понятие субстанции (энергии), а элементарные частицы понимаются как эмерджентные состояния, имеющие второстепенную роль. Приводится система аксиом, задающая основные определения спектра материи. При этом спектр состояний («элементарных частиц») появляется в результате квантования массы (энергии). Выводится массовая формула, зависящая от квантовых чисел, задающих собственные значения операторов Казимира группы Лоренца. Ключевые слова: холизм, редукционизм, спектр масс, массовые формулы, элементарная длина, несепарабельные состояния, дальнодействие В начале была симметрия.
DESCRIPTION Труды пятой сибирской конференции по математическим проблемам физики пространства-вре... more DESCRIPTION Труды пятой сибирской конференции по математическим проблемам физики пространства-времени сложных систем, Новосибирск, 2006г.
DESCRIPTION Труды четвертой сибирской конференции по математическим проблемам физики пространства... more DESCRIPTION Труды четвертой сибирской конференции по математическим проблемам физики пространства-времени сложных систем (ФПВ-2002)/ ред. М. М. Лаврентьева:. Новосибирск, 28--31 июля 2002г. (Изд-во института математики СО РАН, C. 60--89, 2002).
DESCRIPTION Труды третьей сибирской конференции по математическим проблемам физики пространства-в... more DESCRIPTION Труды третьей сибирской конференции по математическим проблемам физики пространства-времени сложных систем (ФПВ-2000)/ ред. М. М. Лаврентьева:. Новосибирск, 20--22 июня 2000г. (Изд-во института математики СО РАН, C. 97--135, 2001).
DESCRIPTION Труды шестой сибирской конференции по математическим проблемам физики пространства-вр... more DESCRIPTION Труды шестой сибирской конференции по математическим проблемам физики пространства-времени сложных систем, Новосибирск, 2007г.
The root structure of the subalgebras of the group algebra of a conformal
group in the framework ... more The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
The structure of the group algebra of a conformal group (the group underlying the group-theoretic... more The structure of the group algebra of a conformal group (the group underlying the group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
The root structure of the subalgebras of the group algebra of a conformal group in the framework ... more The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan–Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
The structure of the group algebra of a conformal group (the group underlying the
group-theoretic... more The structure of the group algebra of a conformal group (the group underlying the group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
What are space and time? What do elementary particles and elements of the periodic table have in ... more What are space and time? What do elementary particles and elements of the periodic table have in common? Keywords: holism, reductionism, hylomorphism, spinors, elementary length, symmetries, long-range action
Аннотация. Что такое пространство и время? Что объединяет элементарные частицы и элементы таблицы... more Аннотация. Что такое пространство и время? Что объединяет элементарные частицы и элементы таблицы Менделеева? Сколько можно делить материю на все меньшие части и почему невозможно верифицировать теорию струн и модель кварков? Эти и другие столь же интригующие вопросы обсуждаются в предлагаемом вниманию читателей интервью с профессором СибГИУ Вадимом Варламовым.
The questions of interpretation of the algebraic formulation of a quantum theory with a binary st... more The questions of interpretation of the algebraic formulation of a quantum theory with a binary structure are considered. The possibility of constructing a quantum theory without using any classical analogies and visual images and mechanical models associated with these analogies is discussed. It is shown that the inconsistency of the quark model, as well as the Bohr model in the theory of the atom, is a consequence of the introduction of classical space-time representations to the subatomic (hadron) level.
We consider a structure of the K-Hilbert space, where K ≃ R is a field of real numbers, K ≃ C is ... more We consider a structure of the K-Hilbert space, where K ≃ R is a field of real numbers, K ≃ C is a field of complex numbers, K ≃ H is a quaternion algebra, within the framework of division rings of Clifford algebras. The K-Hilbert space is generated by the Gelfand-Naimark-Segal construction, while the generating C *-algebra consists of the energy operator H and the generators of the group SU(2, 2) attached to H. The cyclic vectors of the K-Hilbert space corresponding to the tensor products of quaternionic algebras define the pure separable states of the operator algebra. Depending on the division ring K, all states of the operator algebra are divided into three classes: 1) charged states with K ≃ C; 2) neutral states with K ≃ H; 3) truly neutral states with K ≃ R. For pure separable states that define the fermionic and bosonic states of the energy spectrum, the fusion, doubling (complexification) and annihilation operations are determined.
The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional ... more The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional reductional and alternative holistic frameworks. From the holistic viewpoint, substance (the same as energy) is the primary concept and particles are secondary and emergent. An axiomatic system is proposed where the basic notion of the spectrum of matter is defined, and the particle spectrum emerges as a result of the energy/mass quantization. A new mass formula is derived in terms of the quantum numbers related to the Lorentz group Casimir eigenvalues. It is shown that the masses of states in the lepton and hadron sectors of the spectrum of matter are proportional to the electron rest mass (quantum of mass) with an accuracy of 0, 41% on average.
The problem of the mass spectrum of elementary particles is considered from the positions of redu... more The problem of the mass spectrum of elementary particles is considered from the positions of reductionism and holism. It is shown that in the holistic description, the concept of substance (energy) is of paramount importance, and elementary particles are understood as emergent states that play a secondary role. A system of axioms is given that defines the basic definitions of the spectrum of matter. In this case, the spectrum of states ("elementary particles") appears as a result of mass (energy) quantization. A mass formula is derived that depends on the quantum numbers defining the eigenvalues of the Casimir operators of the Lorentz group.
Аннотация. Рассматривается проблема спектра масс элементарных частиц с позиций редукционизма и хо... more Аннотация. Рассматривается проблема спектра масс элементарных частиц с позиций редукционизма и холизма. Показывается, что при холистическом описании первостепенное значение приобретает понятие субстанции (энергии), а элементарные частицы понимаются как эмерджентные состояния, имеющие второстепенную роль. Приводится система аксиом, задающая основные определения спектра материи. При этом спектр состояний («элементарных частиц») появляется в результате квантования массы (энергии). Выводится массовая формула, зависящая от квантовых чисел, задающих собственные значения операторов Казимира группы Лоренца. Ключевые слова: холизм, редукционизм, спектр масс, массовые формулы, элементарная длина, несепарабельные состояния, дальнодействие В начале была симметрия.
DESCRIPTION Труды пятой сибирской конференции по математическим проблемам физики пространства-вре... more DESCRIPTION Труды пятой сибирской конференции по математическим проблемам физики пространства-времени сложных систем, Новосибирск, 2006г.
DESCRIPTION Труды четвертой сибирской конференции по математическим проблемам физики пространства... more DESCRIPTION Труды четвертой сибирской конференции по математическим проблемам физики пространства-времени сложных систем (ФПВ-2002)/ ред. М. М. Лаврентьева:. Новосибирск, 28--31 июля 2002г. (Изд-во института математики СО РАН, C. 60--89, 2002).
DESCRIPTION Труды третьей сибирской конференции по математическим проблемам физики пространства-в... more DESCRIPTION Труды третьей сибирской конференции по математическим проблемам физики пространства-времени сложных систем (ФПВ-2000)/ ред. М. М. Лаврентьева:. Новосибирск, 20--22 июня 2000г. (Изд-во института математики СО РАН, C. 97--135, 2001).
DESCRIPTION Труды шестой сибирской конференции по математическим проблемам физики пространства-вр... more DESCRIPTION Труды шестой сибирской конференции по математическим проблемам физики пространства-времени сложных систем, Новосибирск, 2007г.
The questions of interpretation of the algebraic formulation of a quantum theory with a binary st... more The questions of interpretation of the algebraic formulation of a quantum theory with a binary structure are considered.
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Papers by Vadim Varlamov
group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
long-range action
group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced.
group-theoretic description of the periodic system of chemical elements) is considered within the framework of a twofold covering. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied.
long-range action