Related papers: Three lectures on noncommutative field theories
These notes are based on the lecture the author gave at the workshop 'Geometry of Strings and Fields' held at Nordita, Stockholm. In these notes, I shall cover some topics in both the perturbative and non-perturbative aspects of the…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
Non-Perturbative Quantum Field Theory has played an important role in the study of phenomena where a fermion condensate can appear under certain physical conditions. The familiar phenomenon of electric superconductivity, the color…
In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenwald-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these…
These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an…
In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an…
We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and K-homology, provide a noncommutative…
I discuss two techniques that can be used in the investigation of the properties of ``colliding" and ``non-colliding" anyons.
We study the Wess-Zumino theory on ${\bf R}^3 \times S^1$ where a spatial coordinate is compactified. We show that when the bosonic and fermionic fields satisfy the same boundary condition, the theory does not develop a vacuum energy or…
These lectures provide an introduction to lattice methods for nonperturbative studies of quantum field theories, with an emphasis on Quantum Chromodynamics. Lecture 1 (Ch. 2): gauge field basics Lecture 2 (Ch. 3): Abelian duality with a…
We find exact solitons in a large class of noncommutative gauge theories using a simple solution generating technique. The solitons in the effective field theory description of open string field theory are interpreted as D-branes for any…
A version of $\mathcal{N} = 1$ supersymmetric scalar electrodynamics is considered here, and it is shown that an electrically charged nontopological soliton exists in this model. In addition to the long-range electric field, the soliton…
Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…
We apply the noncommutative fields method to the three-dimensional non-Abelian gauge theory. We find that, first, implementing the noncommutativity between the canonical momenta implies in generation of the non-Abelian Chern-Simons term,…
We propose a physical interpretation of the perturbative breakdown of unitarity in time-like noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of…
Solitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D-branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low-energy effective field theory, which allows for…
We derive an effective field theory for a noncollinear altermagnet and magnons on top of the noncollinear ground state from an altermagnetic Heisenberg model. We obtain the ground-state phase diagram, revealing a noncollinear phase and four…
We discuss non-Abelian bosonization of two and three dimensional fermions using a path-integral framework in which the bosonic action follows from the evaluation of the fermion determinant for the Dirac operator in the presence of a vector…
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum…