1 **Symmetries and Invariances in Physics**

*Centenary* thematic issue

**Editorial annotation**

The physicists’ community celebrates the *centenary* of the publication of “the” *two theorems by Emmy Noether *in 2018*.* There are, approximately at the same time, sixty years of the extension of her two theorems by R. Utiyama (1956 and 1959)

GTR (1915-16) opened the door for the development of the exact formulation of the mutual correspondence between global and local, gauge symmetries on the one side, and variational principles on the other. It is well known that just this inspired F. Klein to encourage E. Noether to elaborate the mathematical bases of the invariances implied in the gravitational theory. The latter are known as the two mathematical theorems by E. Noether on the relation between symmetries and invariances (that were completed four decades later by R. Utiyama). These theorems led physicists further, beyond the borders of the gravitational theory. No new discovery in field theories, particle physics and a few other specialised subdisciplines of physics could avoid the consequences of these theorems formulated on invariances during the last hundred years. Without those developments, one could not identify physical invariances with a class of symmetries. The history of modern physics witnessed an endless sequence of detecting new symmetries and their breaking, then deeper symmetries, and those breakings, and so on. Gauge theories that based these developments opened new and new chapters in the textbooks of physics. Many (undergraduate) textbooks simplify the Noether theorems like any invariance involves a symmetry (or more narrow, a conservation law), and in turn, there corresponds an invariance to any symmetry. In fact, the Noether theorems allow us to look much deeper, and involve much more.

The planned thematic issue of *Symmetry: Culture and Science* would like to pay a tribute by symmetrists to the 100th anniversary of the birth of the two Noether theorems.

– On the one hand, this issue aims at publishing a few specific chapters reviewing relevant issues in the history of physics in the last hundred years. Review papers are welcome.

– On the other hand, it would like to publish papers that describe a few important developments, discoveries, theories and consequent decisive experiments in physics as a result of the Noether theorems and the resulted application of mathematical (algebraic, geometrical) methods. The non-historical type of papers should remain in the domain of mathematical and/or theoretical physics, however the authors are expected to describe the significance of the treated theorems and the methods they offer for the general readers of *Symmetry*. Description of new achievements rooted in the application of invariance principles and their related by-products are welcome. Physics has concentrated mainly on conservation (i.e., invariance under translation in time). However, the Noether theorems, especially the 2nd, allow much more symmetries (invariances). Those possibilities are so far not exploited in physics. References to any such attempt and application are welcome.

Most readers of the Journal are not mathematical physicists, and those who are mathematical physicists are not likely to be specialised in Noether-type fields. Moreover, some are not physicists but are open minded to learning about physical symmetries. In short, equations and math formulas can be applied, but technical details should be avoided. Symbols in the formulas should be explained in the text. The essence of the physical theories explained are expected to be formulated more in words and less in formulas.

Please, follow the *instructions for authors* and use the MS Word (preferred) and TeX style-sheets downloadable from the bottom of the page Instructions. Please, take special care of: (1) the page size, margins, running heads; (2) the use of the built in styles; and (3) follow precisely the given style of references. MS Word users, please, use MathType for formulas and equations.

The *length* of the papers may vary from 6 to 16 pages, including illustrations. Note, the papers will be published both electronically and printed. We can publish *colour* illustrations online, but we can print those illustrations in *b/w* only. The latter means that colours should be made distinguishable in grey-scales after conversion into b/w.

*Deadline* for submissions is 15 October 2017. The papers will be peer-reviewed before decision on their acceptance.

*Submission*: Please, send the manuscripts to the Editor.