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# A new approach to the analysis of a noncommutative Chern-Simons theory

Modern Physics Letters A (Impact Factor: 1.34). 09/2004; DOI: 10.1142/S021773230601927X

Source: arXiv

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**ABSTRACT:**A novel approach to the analysis of the gravitational well problem from the point of view of a second quantized description is discussed. The second quantized formalism enables us to study the effect of time-space non-commutativity in the gravitational well scenario; this study is hitherto unavailable in the literature. The corresponding first quantized theory reveals a leading order perturbation term of non-commutative origin. The latest experimental findings are used to estimate an upper bound on the time-space non-commutative parameter. Our results are found to be consistent with the order of magnitude estimations of other NC parameters reported earlier.European Physical Journal C 05/2007; 51(1):199-205. · 5.44 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string theoretic models. The manifestations of gauge symmetries and their interconnection with the diffeomorphism invariances have been discussed in the context of different generally covariant models like string, membrane, $p-$brane and metric gravity. Analysis of interacting string with proper inclusion of the stringy boundary conditions led to the noncommutative nature of the string coordinates. In the second part of the thesis the emphasis was primarily on the impact of gauge symmetries on the field theories defined over noncommutative space-time. The correspondence between the NC gauge symmetry and ordinary gauge symmetry manifest by Seiberg--Witten maps between the NC gauge fields and ordinary gauge fields have been used to construct equivalent commutative theories describing the original NC gauge theories. Using this commutative equivalent approach we have analysed several NC gauge field theories of current interest. A upper-bound on the time-space noncommutative parameter has also been worked out. Comment: 147 pages, Ph.D. thesis (2009), Advisor : Pradip Mukherjee09/2009; -
##### Article: Noncommutative Solitons of Gravity

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**ABSTRACT:**We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek noncommutative solitons in noncommutative scalar field theories. Some of those solutions correspond to bubbles of spacetimes, or represent dimensional reduction. The solution which interpolates $G_{\mu\nu}=0$ and Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter $\theta$, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity. Comment: 29 pages, 5 figures. v2: minor corrections done in Section 3.1 and Appendix, references added. v3, v4: typos correctedClassical and Quantum Gravity 11/2009; · 3.10 Impact Factor

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