On two-loop effective action of 2d sigma model

Article Physics, Multidisciplinary

Ordered exponential and its features in Yang-Mills effective action

A. Ivanov et al.

Summary: In this paper, non-trivial relations for ordered exponentials on smooth Riemannian manifolds are discussed. As an application, the dependence of the four-dimensional quantum Yang-Mills effective action on the special gauge transformation with respect to the background field is studied. Open questions regarding the structure of divergences for a special type of regularization in the presence of the background field formalism are also formulated.

COMMUNICATIONS IN THEORETICAL PHYSICS (2023)

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Article Physics, Multidisciplinary

Explicit Cutoff Regularization in Coordinate Representation

Aleksandr Ivanov

Summary: This paper studies a special type of cutoff regularization in the coordinate representation. It demonstrates how this approach unites various concepts and properties, such as explicit cutoff, spectral representation, homogenization, and covariance. In addition, new formulae are presented to work with the regularization, along with additional calculations of the infrared asymptotics for certain regularized Green's functions in the Yang-Mills theory and Sigma-model.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

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Article Physics, Multidisciplinary

Special functions for heat kernel expansion

A. Ivanov et al.

Summary: This paper studies an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold. Recurrence relations for the Seeley-DeWitt coefficients are used to construct two families of special functions, which are then used to study the expansion of a local heat kernel for the inverse Laplace operator. Important properties of the new functions are shown, and various applications in theoretical physics, including a decomposition of local Green's functions, are described.

EUROPEAN PHYSICAL JOURNAL PLUS (2022)

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Article Physics, Particles & Fields

Formula for two-loop divergent part of 4-D Yang-Mills effective action

A. Ivanov et al.

Summary: In this paper, we investigate the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for this contribution and test its consistency with results from other works using dimensional regularization and cutoff regularization.

EUROPEAN PHYSICAL JOURNAL C (2022)

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