arXiv subjects

H. Malavazzi

Publications and source records attributed to H. Malavazzi.

3 recordsLinked to original sources

arXiv2026

The Hidden Symmetries of Yang-Mills Theory in (1+1)-dimensions

We present an integral formulation of classical Yang-Mills theory coupled to fermionic and scalar matter fields in (1+1)-dimensional Minkowski spacetime. By reformulating the local dynamics in terms of loop-space holonomies, we demonstrate that the path independence of the holonomy eigenvalues constitutes a conservation law, yielding an infinite hierarchy of gauge-invariant, dynamically conserved charges. While a zero-curvature equation is associated with a necessary condition for this path invariance, we note that it is not strictly sufficient on its own. Employing a first-order symplectic formalism, we show that these non-abelian charges generate global symmetry transformations on the fundamental phase-space variables. We rigorously prove that these transformations preserve the physical dynamics, leaving the total Hamiltonian invariant up to first-class constraints. Furthermore, an analysis of the Poisson algebra reveals that these conserved charges are in involution, provided the boundary integration constant lies within the center of the gauge group. This exact, lower-dimensional framework provides a highly tractable setting to investigate the algebraic structures of these hidden symmetries and the meaning of the conserved charges as physical observables, establishing a classical foundation for exploring their role in the quantum regime, such as in strongly coupled lattice gauge theories.

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arXiv2025

The Hidden Symmetries of Yang-Mills Theory in (3+1)-dimensions

We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3+1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number of conserved charges in involution. Such structures live in the space of non-abelian electric and magnetic charges, and are based on flat connections in generalized loop spaces, presenting an R-matrix, and Sklyanin relation. We present two novel symmetries of Yang-Mills theories. The first one corresponds to global transformations generated by the infinity of those conserved charges under the Poisson brackets. The gauge and matter fields, as well as Wilson lines and fluxes, have interesting transformation laws under such a global symmetry. The second one corresponds to symmetries of the integral Yang-Mills equations, which lead to the conserved charges. They generate an infinite-dimensional group, where the elements are holonomies of connections on the loop space of functions from the circle S^1 to the space-time. Our approach certainly applies to the Standard Model of the Fundamental Interactions. The conserved charges are gauge invariant, and so, in the case of QCD, they are color singlets and perhaps are not confined. Therefore, the hadrons may carry such charges. Our results open up the way for the construction of non-perturbative methods for Yang-Mills theories.

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arXiv2021

A Generalised Self-Duality for the Yang-Mills-Higgs System

Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space R^3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ansätz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ansätz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields.

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