Special generalized densities and propagators: A geometric account

Canarutto, Daniel

doi:10.1142/s0219887815300044

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…A natural Lagrangian yielding a first order generalized Dirac equation can be exhibited; in flat spacetime, a plain wave solution in the main sector Z determines the solution in the ghost sectors. 16 • The electroweak theory can be formulated within two-spinor geometry, without dealing with structure groups, by adding one main ingredient: the isospin bundle I M , a Hermitian bundle with two-dimensional complex fibres. The fermion bundle is then assumed to be the fibred direct product of a right-handed and left-handed sectors, 17 that is…”

Section: Two-spinor Bundle and Spacetime Geometrymentioning

confidence: 99%

Gauge field theory without groups

Canarutto

2020

Preprint

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Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book [1]. By proposing a change of perspective about the roles and relative importance of several notions, this approach seeks to obtain an overall clarification of foundational matters. In particular, by consistently relying on natural differential geometry, the role of groups is shown to be downgradable to secondary.

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Section: Two-spinor Bundle and Spacetime Geometrymentioning

confidence: 99%

Gauge field theory without groups

Canarutto

2020

Preprint

Self Cite

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“…Moreover, he dealt with the case of electroweak interactions. Additionally, in [10], Canarutto provided a suitable formulation of the fundamental mathematical concepts with respect to quantum field theory. Such a paper presents a natural application of the concept of semi-vector spaces and semi-algebras.…”

Section: Introductionmentioning

confidence: 99%

On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata

La Guardia,

Chagas,

Lenzi

et al. 2024

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In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers R0+. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topological properties of semi-vector spaces, such as completeness and separability, are also investigated here. New families of semi-vector spaces derived from the semi-metric, semi-norm and semi-inner product, among others, are exhibited. Furthermore, we show several new results concerning semi-algebras. After this theoretical approach, we apply such a theory in fuzzy automata. More precisely, we describe the semi-algebra of A-fuzzy regular languages and we apply the theory of fuzzy automata for counting patterns in DNA sequences.

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“…Moreover, he dealt with the case of electroweak interactions. Additionally, in [2], Canarutto provided a suitable formulation of the fundamental mathematical concepts with respect to quantum field theory. Such a paper presents a natural application of the concept of semi-vector spaces and semi-algebras.…”

Section: Introductionmentioning

confidence: 99%

On semi-vector spaces and semi-algebras

Guardia¹,

Chagas²,

Lenzi³

et al. 2021

Preprint

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It is well-known that the theories of semi-vector spaces and semi-algebras -which were not much studied over time -are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to provide new mathematical tools to investigate properties and new results on fuzzy systems. In this paper we investigate the theory of semi-vector spaces over the semi-field of nonnegative real numbers R + 0 . We prove several results concerning semi-vector spaces and semi-linear transformations. Moreover, we introduce in the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing in some cases how to compute them. Topological properties of semi-vector spaces such as completeness and separability are also investigated. New families of semivector spaces derived from semi-metric, semi-norm, semi-inner product, among others are exhibited. Additionally, some results on semi-algebras are presented.

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Special generalized densities and propagators: A geometric account

Cited by 3 publications

References 12 publications

Gauge field theory without groups

Gauge field theory without groups

On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata

On semi-vector spaces and semi-algebras

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