QUASILOCALITY OF GAUGE CHARGES

S. Ye. Samokhvalov, A. A. Gryshchenko

Abstract


All fundamental interactions known today are gauge. This means that the equations of these theories are symmetric with respect to the corresponding gauge groups. On the other hand, according toE. Noether's theorem, each symmetry corresponds to a conserved quantity. For gauge symmetries, these are the so-called gauge charges. An important property of charges is quasilocality, which means that the current of a given charge is expressed through the divergence of the antisymmetric tensor, which is called its superpotential. This provides a "holographic" property of charge, i.e. the ability to determine its total value, limited by a two-dimensional surface, through the value of the superpotential on the surface. In the work "Group- theoretical basis of the holographic principle" it was proved that in gauge theories with Lagrangians, wich depend on field variables and their derivatives not higher than the first order, and infinitesimal transformations of fields depend on not higher than the first derivatives of gauge parameters, gauge charges are quasilocal. In this paper we generalize the results of this work for the case of arbitrary orders of derivatives.

It was shown that in the conditions under consideration the gauge charge Qa, associated with the currents Jσα, are conserved, too. An important theorem is proved that in the gauge theory of the generalized gauge group GgM the gauge charges Qa are quasilocal, so their currents Jµα have superpotentials Sµνα. One of the Noether’s identity allows us to express the current through the variations of the Lagrangian derivative and the divergence of the superpotential and the divergence of the current through a linear combination of variational derivatives of Lagrangian and their derivatives.

The proved theorem and the method of its proof give an algorithm for constructing currents of gauge charges, as well as their superpotentials for a wide range of theories with gauge symmetries.


Keywords


quasilocality; gauge theory; superpotential; symmetry; gauge charges

References


Noether E. Invariant variation problems. Transport theory and statistical physics. 1971. № 1(3). P.183-207.

Szabados L.B. Quasi-local energy-momentum and angular momentum in GR: A review article. Living rev. relativity. 2004. № 4. P.1-140.

Самохвалов С.Є. Теоретико-групове підґрунтя голографічного принципу. Математичне моделювання, 2010. № 2(23). С.7-11.




DOI: https://doi.org/10.31319/2519-2884.36.2020.19

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Copyright (c) 2020 S. Ye. Samokhvalov, A. A. Gryshchenko

ISSN (print) 2519-2884

ISSN (online) 2617-8389