Symmetries and Group Theory in Particle Physics

Costa, Giovanni; Fogli, G. L.

doi:10.1007/978-3-642-15482-9

Cited by 29 publications

(51 citation statements)

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“…But unfortunately, this is not the case. The order parameter space of 3D orientations is also not simply connected [37]. Indeed, it is usually considered as either the full 3D sphere or the surface of the 4D sphere, both with antipodal points equated.…”

Section: Discussionmentioning

confidence: 99%

Topological defects in two-dimensional orientation-field models for grain growth

et al. 2017

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Standard two-dimensional orientation-field-based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply connected. This topological property has important consequences for the resulting multigrain structures: (i) trijunctions may be singular; (ii) for each pair of grains there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can be interpreted in the classical picture of grain boundaries, (ii) and therefore (iii) cannot. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two formulations of the model. The first is based on a three-component unit vector field, while in the second we utilize a two-component vector field with an additional potential. In both cases, the additional degree of freedom introduced makes the order parameter space simply connected, which removes the topological stability of these defects.

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Section: Discussionmentioning

confidence: 99%

Topological defects in two-dimensional orientation-field models for grain growth

et al. 2017

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“…This theorem indicates that every process in nature exactly conserves the three combined operators C, P and T . A further consequence is that particle-antiparticle partners have exactly the same mass and lifetime, and exactly opposite magnetic moments [50,51]. Many tests of these matter-antimatter symmetries have been sented here involve the mass difference between K 0 and K 0 [58,59], the g-2 for the positron [60,61,62] and muon [63,64], the charge-to-mass ratio and g-factor of the antiproton [65,66], and two forthcoming comparisons between neutral atoms of antihydrogen and hydrogen [67]:…”

Section: Antimatter and Symmetrymentioning

confidence: 96%

“…Symmetries play a major role in our understanding of many aspects of the structure of matter at the most elementary level, and play an essential role in our understanding of antimatter [50,51]. The charge conjugation operator C changes a particle into its antiparticle; thus, it reverses the sign of electric charge, baryon number, lepton number, as well as strangeness and heavy quark flavor quantum numbers.…”

Section: Antimatter and Symmetrymentioning

confidence: 99%

Antinuclei in heavy-ion collisions

et al. 2018

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We review progress in the study of antinuclei, starting from Dirac's equation and the discovery of the positron in cosmic-ray events. The development of proton accelerators led to the discovery of antiprotons, followed by the first antideuterons, demonstrating that antinucleons bind into antinuclei. With the development of heavy-ion programs at the Brookhaven AGS and CERN SPS, it was demonstrated that central collisions of heavy nuclei offer a fertile ground for research and discoveries in the area of antinuclei. In this review, we emphasize recent observations at Brookhaven's Relativistic Heavy Ion Collider and at CERN's Large Hadron Collider, namely, the antihypertriton and the antihelium-4, as well as measurements of the mass difference between light nuclei and antinuclei, and the interaction between antiprotons. Physics implications of the new observations and different production mechanisms are discussed. We also consider implications for related fields, such as hypernuclear physics and spacebased cosmic-ray experiments.

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“…In addition, Noether's work except of its simplicity had a second novelty by alloying the continuous transformation to depend also on the derivatives of the dependent function, which was the first generalization of the context of symmetry from point transformations to higher-order transformations. Symmetries play an important role in various theories of physics, from analytical mechanics [22], to particle physics [23,24], and gravitational physics [1,25].…”

Section: Introductionmentioning

confidence: 99%

Symmetries of Differential Equations in Cosmology

2018

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Abstract:The purpose of the current article is to present a brief albeit accurate presentation of the main tools used in the study of symmetries of Lagrange equations for holonomic systems and subsequently to show how these tools are applied in the major models of modern cosmology in order to derive exact solutions and deal with the problem of dark matter/energy. The key role in this approach are the first integrals of the field equations. We start with the Lie point symmetries and the first integrals defined by them, that is, the Hojman integrals. Subsequently, we discuss the Noether point symmetries and the well-known method for deriving the Noether integrals. By means of the Inverse Noether Theorem, we show that, to every Hojman quadratic first integral, it is possible to associate a Noether symmetry whose Noether integral is the original Hojman integral. It is emphasized that the point transformation generating this Noether symmetry need not coincide with the point transformation defining the Lie symmetry which produces the Hojman integral. We discuss the close connection between the Lie point and the Noether point symmetries with the collineations of the metric defined by the kinetic energy of the Lagrangian. In particular, the generators of Noether point symmetries are elements of the homothetic algebra of that metric. The key point in the current study of cosmological models is the introduction of the mini superspace, which is the space that is defined by the physical variables of the model, which is not the spacetime where the model evolves. The metric in the mini superspace is found from the kinematic part of the Lagrangian and we call it the kinetic metric. The rest part of the Lagrangian is the effective potential. We consider coordinate transformations of the original mini superspace metric in order to bring it to a form where we know its collineations, that is, the Killing vectors, the homothetic vector, etc. Then, we write the field equations of the cosmological model and we use the connection of these equations with the collineations of the mini superspace metric to compute the first integrals and subsequently to obtain analytic solutions for various allowable potentials and finally draw conclusions about the problem of dark energy. We consider the ΛCDM cosmological model, the scalar field cosmology, the Brans-Dicke cosmology, the f (R) gravity, the two scalar fields cosmology with interacting scalar fields and the Galilean cosmology. In each case, we present the relevant results in the form of tables for easy reference. Finally, we discuss briefly the higher order symmetries (the contact symmetries) and show how they are applied in the cases of scalar field cosmology and in the f (R) gravity.

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Symmetries and Group Theory in Particle Physics

Cited by 29 publications

References 0 publications

Topological defects in two-dimensional orientation-field models for grain growth

Topological defects in two-dimensional orientation-field models for grain growth

Antinuclei in heavy-ion collisions

Symmetries of Differential Equations in Cosmology

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