Physics and Symmetries of Commutative and Noncommutative Quantum Field Theory

Dear Colleagues,

Quantum field theory (QFT) is a theoretical framework that combines classical field theory and quantum mechanical principles to describe the nature around us. It has been extremely successful in constructing physical models in particle physics (especially the QED and Standard model) and condensed matter physics, and has important implications in quantum aspects of gravity theories.

QFT is a result of constructing a theory that describes the many-particle sys-tems in accordance with the quantum mechanical principles together with the principles of special relativity.  The Poincaré symmetry is thus incorporated in the theory from the very beginning.  It is believed that for particles with very high energies the gravity effects become significant, so that these particles no longer "see" the spacetime as smooth and continuous, but instead they see it as quantized or fuzzy. The QFT constructed on such deformed manifolds requires a new framework. Such framework could be provided via the noncommutative geometry, where the search for the diffeomorphisms leaving spacetime invariant leads to deformation of Poincaré symmetry.

 Even though QFT has had much success in explaining phenomenological phenomena, its mathematical rigor (in some aspects) is still a topic of interest and work for many mathematical physicists. Noncommutative geometry and noncommutative QFTs have promising results in explaining the geometry of particle interactions, providing a framework even for quantum aspects of gravity and even lifting the theory to a more rigorous formulation.

This Special Issue will publish contributions on various aspects of commutative and noncommutative QFTs, studying the interplay between them, symmetries and their generalizations, and their applications in the quantum aspects of spacetime. The articles are expected to present some new or recent results in the field along with a general review of the problem and a history of the problem in matter.

Dr. Tajron Jurić
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.