About the Structure of Meson Algebras

Helmstetter, Jacques; Micali, Artibano

doi:10.1007/s00006-010-0213-0

Cited by 8 publications

(6 citation statements)

References 9 publications

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“…In particular, it is important to emphasize that the DKP field is often employed in nuclear physics to describe mesons [21], when it is possible to say that it has a mesonic algebraic structure [67]. But the DKP fields are described by the DKP algebra, while the fermionic field obeys a Clifford algebra.…”

Section: Discussionmentioning

confidence: 99%

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

et al. 2018

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The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Dirac's methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Green's functions are obtained through functional methods and the theory's renormalizability is also detailed presented. Next, the radiative corrections for the Green's functions at α-order are computed; and, as it turns out, an unexpected m P -dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at α 2 -order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higherorder contributions. Lastly, an energy range where the theory is well defined: m 2 k 2 < m 2 p was also found by evaluating the effective coupling for the GSDKP. * rbufalo@ift.unesp.br † cardoso@ift.unesp.br ‡ nogueira@ift.unesp.br § pimentel@ift.unesp.br 1 arXiv:1510.04877v1 [hep-th] 16 Oct 20151 The historical development of this theory, among others, can be found in [1,2]. 2 Forsooth, Géhéniau decomposed Petiau's sixteen-dimensional algebra in terms of irreducible representations of ten dimensions (representing particles of spin 1), five dimensions (representing particles of spin 0), and a trivial representation without physical meaning of one dimension [7].3 This formalism can be extended to describe non-Abelian and gravitational fields [11].

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Section: Discussionmentioning

confidence: 99%

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

et al. 2018

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“…, and the identity (1.10) is a consequence of M (3) =0 in A (1) , but requires some manipulation of the decomposed identity map for 3-adic tensors to prove. Larger Clifford and Kemmer algebras which contain their {S a } counterparts are definable on the physical three-space [14,35,36] using modified identities (1.9) and (1.10), however it is unclear if any instructive comparisons can be made between them and the spin algebras.…”

Section: Mathematical Comparison With Other Non-relativistic Modelsmentioning

confidence: 99%

An algebraic theory of non-relativistic spin

Bradshaw

2024

Phys. Scr.

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In this paper we present a new, elementary derivation of non-relativistic spin using exclusively real algebraic methods. To do this, we formulate a novel method to decompose the domain of a real endomorphism according to its algebraic properties. We reveal non-commutative multipole tensors as the primary physically meaningful observables of spin, and indicate that spin is fundamentally geometric in nature. In so doing, we demonstrate that neither dynamics nor complex numbers are essential to the fundamental description of spin.

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“…If Z denotes the orbit of x in the retraction of A, then I Z (A/Rad(A)) is non-commutative, which shows that a single retraction in Proposition 10 does not suffice. Note that in constrast to the exterior algebra (V ), it is not enough to assume the relation bab = 0 for the elements of the subspace V := F 2 x ⊕ F 2 y of A, which would lead to the meson algebra B(V ), an algebra [20,24,26] with an additional basis element x 2 y 2 . In A, this element vanishes since (x + y)x(x + y)y = 0.…”

Section: Definitionmentioning

confidence: 99%

Two theorems on balanced braces

Rump¹

2021

Proceedings of the Edinburgh Mathematical Society

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Two theorems of Gateva-Ivanova [Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups, Adv. Math. 338 (2018), 649–701] on square-free set-theoretic solutions to the Yang–Baxter equation are extended to a wide class of solutions. The square-free hypothesis is almost completely removed. Gateva-Ivanova and Majid's ‘cyclic’ condition ${\boldsymbol {\rm lri}}$ is shown to be equivalent to balancedness, introduced in Rump [A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation, Adv. Math. 193 (2005), 40–55]. Basic results on balanced solutions are established. For example, it is proved that every finite, not necessarily square-free, balanced brace determines a multipermutation solution.

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About the Structure of Meson Algebras

Cited by 8 publications

References 9 publications

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

An algebraic theory of non-relativistic spin

Two theorems on balanced braces

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