# Three lectures on noncommutative field theories

@article{Schaposnik2004ThreeLO, title={Three lectures on noncommutative field theories}, author={Fidel A. Schaposnik}, journal={arXiv: High Energy Physics - Theory}, year={2004} }

Classical and quantum aspects of noncommutative field theories are discussed. In particular, noncommutative solitons and instantons are constructed and also d=2,3 noncommutative fermion and bosonic (Wess-Zumino-Witten and Chern-Simons)theories are analyzed.

## 13 Citations

Theories on noncommutative spaces and deformed symmetries

- Physics
- 2010

In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations…

Symmetries of Field Theories on the Noncommutative Plane

- Mathematics, Physics
- 2005

We report new developments concerning the symmetry properties and their actions on special solutions allowed by certain field theory models on the noncommutative plane. In particular, we seek…

Vortex solutions in the noncommutative torus

- Mathematics
- 2006

Vortex configurations in the two-dimensional torus are considered in noncommutative space. We analyze the BPS equations of the Abelian Higgs model. Numerical solutions are constructed for the…

On the unitarity of higher derivative and nonlocal theories

- Mathematics, Physics
- 2007

We consider two simple models of higher derivative and nonlocal quantum systems. It is shown that, contrary to some claims found in literature, they can be made unitary.

Bogomolny equations for vortices in the noncommutative torus

- Mathematics
- 2005

We derive Bogomolny-type equations for the abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary…

One-loop effects in a self-dual planar noncommutative theory

- Mathematics
- 2007

We study the UV properties, and derive the explicit form of the one-loop effective action, for a noncommutative complex scalar field theory in 2+1 dimensions with a Grosse-Wulkenhaar term, at the…

Heat kernel, effective action and anomalies in noncommutative theories

- Physics
- 2005

Being motivated by physical applications (as the 4 model) we calculate the heat kernel coefficients for generalised laplacians on the Moyal plane containing both left and right multiplications. We…

Deformed Kac–Moody algebra and noncommutative Fermi theory in two dimensions

- MathematicsInternational Journal of Modern Physics A
- 2021

Starting from noncommutative Fermi theory in two dimensions, we construct a deformed Kac–Moody algebra between its vector and chiral currents. The higher-order corrections to the deformed Kac–Moody…

On the Consistency of Twisted Gauge Theory 1

- Physics
- 2007

It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry. PACS number(s):

## References

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Exact noncommutative solitons

- Physics
- 2000

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…

Thermal effects in perturbative noncommutative gauge theories

- Physics
- 1999

The thermodynamics of gauge theories on the noncommutative plane is studied in perturbation theory. For U(1) noncommutative Yang-Mills we compute the first quantum correction to the ideal gas free…

Instantons on Noncommutative ℝ4, and (2,0) Superconformal Six Dimensional Theory

- Physics, Mathematics
- 1998

Abstract:We show that the resolution of moduli space of ideal instantons parameterizes the instantons on noncommutative ℝ4. This moduli space appears to be the Higgs branch of the theory of…

Noncommutative 3 Dimensional Soliton from Multi-instantons

- Mathematics
- 2004

We extend Manton’s proposal [1] of obtaining monopole configurations from infinite charge instantons, to noncommutative space-times. Using this approach, and starting from the noncommutative selfdual…

Non BPS noncommutative vortices

- Mathematics
- 2003

We construct exact vortex solutions to the equations of motion of the abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point.…

The moduli space of noncommutative vortices

- Mathematics
- 2002

The Abelian Higgs model on the noncommutative plane admits both BPS vortices and non-BPS fluxons. After reviewing the properties of these solitons, we discuss several new aspects of the former. We…