Star product and invariant integration for Lie Type noncommutative spacetimes

Gauge theory on the q-deformed two-dimensional Euclidean plane [Formula: see text] is studied using two different approaches. We first formulate the theory using the natural algebraic structures on [Formula: see text], such as a covariant differential calculus, a frame of one-forms and invariant integration. We then consider a suitable star product, and introduce a natural way to implement the Seiberg–Witten map. In both approaches, gauge invariance requires a suitable "measure" in the action, breaking the Eq(2)-invariance. Some possibilities to avoid this conclusion using additional terms in the action are proposed.

Download Full-text

Correction to: Star-Product Formalism for the Probability and Mean-Value Representations of Qudits

Journal of Russian Laser Research ◽

10.1007/s10946-020-09937-y ◽

2021 ◽

Author(s):

Peter Adam ◽

Vladimir A. Andreev ◽

Margarita A. Man’ko ◽

Vladimir I. Man’ko ◽

Matyas Mechler

Keyword(s):

Star Product ◽

Mean Value

Download Full-text

Topological correlators and surface defects from equivariant cohomology

Journal of High Energy Physics ◽

10.1007/jhep09(2020)185 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Rodolfo Panerai ◽

Antonio Pittelli ◽

Konstantina Polydorou

Keyword(s):

Quantum Mechanics ◽

Equivariant Cohomology ◽

Surface Defects ◽

Star Product ◽

Three Dimensional ◽

Three Dimensions ◽

Dimensional System ◽

The Novel ◽

One Dimensional ◽

Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Download Full-text