arXiv subjects

Joao Baptista

Publications and source records attributed to Joao Baptista.

6 recordsLinked to original sources

arXiv2026

The geometry of CP symmetry in Kaluza-Klein models

We investigate the free, massless Dirac equation $Dψ= 0$ on a higher-dimensional manifold $M_4 \times K$ equipped with a submersion metric. These background metrics generalize the Kaluza ansatz. They encode 4D massive gauge fields and Higgs-like scalars, alongside the usual metric on $M_4$ and massless gauge fields. In this framework, the interactions of 4D gauge fields with spinors are determined by the Kosmann derivatives of the spinors' internal components. For massive gauge fields, however, those derivatives do not commute with the internal Dirac operator. This causes a natural misalignment between the mass eigenspinors and the spinor representation bases. Thus, a complex, infinite-dimensional, CKM-like matrix emerges directly from the Dirac equation on $M_4 \times K$. Examining this general framework, we prove that it nevertheless cannot produce CP violation in 4D for any compact $K$ with constant internal geometry. The same holds for the Weyl equation unless $\dim K = 2 \pmod{4}$. Using the language of spin geometry, we develop detailed descriptions of parity and conjugation symmetries in KK models. We find that the gauge representations are always self-conjugate when $\dim K \neq 1 \pmod{4}$ (hence anomaly-free), discuss fermion generations, and introduce a new Lie derivative of spinors along non-Killing vector fields induced by actions of compact groups.

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arXiv2026

Chiral interactions of fermions and massive gauge fields in Kaluza-Klein models

In Kaluza-Klein theory, gauge fields on $M_4$ arise as components of a higher-dimensional metric defined on $M_4 \times K$. The traditional expectation is that all the gauge fields of the Standard Model are linked to exact Killing vector fields on the internal space. This paper questions that assumption and investigates the properties of 4D gauge fields linked to non-Killing fields on $K$. It is shown that they have massive yet arbitrarily light bosons; they can mix fermions with different masses; and they can have asymmetric couplings to left- and right-handed fermions. None of these properties is easily satisfied by gauge fields linked to internal isometries. So the massive gauge fields produced in this manner circumvent traditional no-go arguments and offer a geometric source of chiral interactions with fermions. This may help to model the weak force within the Kaluza-Klein framework. Technically, the paper uses the language of spin geometry and Riemannian submersions. It studies the higher-dimensional Dirac operator with non-trivial background metrics. The results are derived for a general $K$. They are illustrated explicitly in the simpler cases where $K$ is the two-sphere and the two-torus.

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arXiv2024

Test particles in Kaluza-Klein models

Geodesics in general relativity describe the behaviour of test particles in a gravitational field. In 5D Kaluza-Klein, geodesics reproduce the Lorentz force motion of particles in an electromagnetic field. This paper studies geodesic motion on a higher-dimensional $M_4 \times K$ with background metrics encoding general 4D gauge fields and Higgs-like scalars. It shows that the classical mass and charge of a test particle become variable quantities when the geodesic traverses regions of spacetime with massive gauge fields, such as the weak force field, or with non-constant Higgs scalars. This agrees with the physical fact that interactions mediated by massive bosons can change the mass and charge of particles. The variation rates of mass and charge along a geodesic are given by natural geometric formulae. In regions where mass is preserved, there are additional constants of motion, one for every abelian or simple summand in the Killing algebra of $K$. The last part of the paper discusses traditional difficulties of Kaluza-Klein models, such as the low $q / m$ ratios in the 5D model. It suggests possible ways to circumvent them. It also remarks the naturalness of a model in which elementary particles always travel at the speed of light in higher dimensions.

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arXiv2024

Internal symmetries in Kaluza-Klein models

The usual approach to Kaluza-Klein considers a spacetime of the form $M_4 \times K$ and identifies the isometry group of the internal vacuum metric, $g_K^0$, with the gauge group in four dimensions. In these notes we discuss a variant approach where part of the gauge group does not come from full isometries of $g_K^0$, but instead comes from weaker internal symmetries that only preserve the Einstein-Hilbert action on $K$. Then the weaker symmetries are spontaneously broken by the choice of vacuum metric and generate massive gauge bosons within the Kaluza-Klein framework, with no need to introduce ad hoc Higgs fields. Using the language of Riemannian submersions, the classical mass of a gauge boson is calculated in terms of the Lie derivatives of $g_K^0$. These massive bosons can be arbitrarily light and seem able to evade the standard no-go arguments against chiral fermionic interactions in Kaluza-Klein. As a second main theme, we also question the traditional assumption of a Kaluza-Klein vacuum represented by a product Einstein metric. This should not be true when that metric is unstable. In fact, we argue that the unravelling of the Einstein metric along certain instabilities is a desirable feature of the model, since it generates inflation and allows some metric components to change length scale. In the case of the Lie group $K = SU(3)$, the unravelling of the bi-invariant metric along an unstable perturbation also breaks the isometry group from $( SU(3) \times SU(3)) / Z_3$ down to $( SU(3) \times SU(2) \times U(1) )/ Z_6$, the gauge group of the Standard Model. We briefly discuss possible ways to stabilize the internal metric after that first symmetry breaking and produce an electroweak symmetry breaking at a different mass scale.

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arXiv2023

Higher-dimensional routes to the Standard Model bosons

In the old spirit of Kaluza-Klein, we consider a spacetime of the form $P = M_4 \times K$, where $K$ is the Lie group $\mathrm{SU}(3)$ equipped with a left-invariant metric that is not fully right-invariant. This metric has a ${\rm U}(1) \times \mathrm{SU}(3)$ isometry group, corresponding to the massless gauge bosons, and depends on a parameter $ϕ$ with values in a subspace of $\mathfrak{su}(3)$ isomorphic to $\mathbb{C}^2$. It is shown that the classical Einstein-Hilbert Lagrangian density $R_P - 2 Λ$ on the higher-dimensional manifold $P$, after integration over $K$, encodes not only the Yang-Mills terms of the Standard Model over $M_4$, as in the usual Kaluza-Klein calculation, but also a kinetic term $|{\mathrm d}^A ϕ|^2$ identical to the covariant derivative of the Higgs field. For $Λ$ in an appropriate range, it also encodes a potential $V(| ϕ|^2)$ having absolute minima with $|ϕ_0|^2 \neq 0$, thereby inducing mass terms for the remaining gauge bosons. The classical masses of the resulting Higgs-like and gauge bosons are explicitly calculated as functions of the vacuum value $|ϕ_0|^2$ in the simplest version of the model. In more general versions, the classical values of the strong and electroweak gauge coupling constants are given as functions of the parameters of the left-invariant metric on $K$.

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arXiv2021

Higher-dimensional routes to the Standard Model fermions

In the old spirit of Kaluza-Klein, we consider a spacetime of the form $P = M_4 \times K$, where $K$ is the Lie group $\mathrm{SU}(3)$ equipped with a left-invariant metric that is not fully right-invariant. We observe that a complete generation of fermionic fields can be encoded in the 64 components of a single spinor over the 12-dimensional spacetime. The behaviour of the spinorial function along the internal space $K$ can be chosen so that, after pairing and fibre-integration over $K$, the resulting Dirac kinetic terms in four dimensions couple to the $\mathfrak{u}(1) \oplus \mathfrak{su}(2) \oplus \mathfrak{su}(3)$ gauge fields in the exact chiral representations present in the Standard Model. Although we describe the action of the internal Dirac operator on the 12-dimensional spinor, the full calculation of the fermionic mass terms produced by the model is longer and is not carried out here. We calculate instead the action of the internal Laplace operator on the spinor components.

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