# Quantization of the Nonlinear Sigma Model Revisited

@article{Nguyen2014QuantizationOT, title={Quantization of the Nonlinear Sigma Model Revisited}, author={Timothy Nguyen}, journal={arXiv: Mathematical Physics}, year={2014} }

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space…

## 8 Citations

### BV Quantization of the Rozansky–Witten Model

- Mathematics
- 2015

We investigate the perturbative aspects of Rozansky–Witten’s 3d $${\sigma}$$σ-model (Rozansky and Witten in Sel Math 3(3):401–458, 1997) using Costello’s approach to the Batalin–Vilkovisky (BV)…

### THE PERTURBATIVE APPROACH TO PATH INTEGRALS: A SUCCINCT MATHEMATICAL TREATMENT

- Mathematics
- 2016

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper…

### Homotopy RG Flow and the Non-Linear $\sigma$-model

- Mathematics
- 2017

The purpose of this note is two give a mathematical treatment to the low energy effective theory of the two-dimensional sigma model. Perhaps surprisingly, our low energy effective theory encodes much…

### Homotopy RG flow and the non-linear -model

- Mathematics
- 2018

A BSTRACT . The purpose of this note is to give a mathematical treatment to the low energy effective theory of the two-dimensional sigma model. Perhaps surprisingly, our low energy effective theory…

### LIE ALGEBROIDS AS $L_{\infty }$ SPACES

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2018

In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an…

### The normalized second order renormalization group flow on closed surfaces

- Mathematics
- 2016

We study a normalized version of the second order renormalization group flow on closed Riemannian surfaces. We discuss some general properties of this flow and establish several basic formulas. In…

### A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

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