Related papers: On Localization and Regularization
We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…
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 understanding of how Wick's theorem allows…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
The path integral formulation can reproduce the right energy spectrum of the harmonic oscillator potential, but it cannot resolve the Coulomb potential problem. This is because the path integral cannot properly take into account the…
The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review…
In this paper, we introduce the Bessel-Struve transform, we establish an inversion theorem of the Weyl integral transform associated with this transform, in the case of half integers, we give a characterization of the range of…
Review of localization in geometry: equivariant cohomology, characteristic classes, Atiyah-Bott formula, Atiyah-Singer equivariant index formula, Mathai-Quillen formalism
We show that two elementary worldline path integrals-the thermal partition function of the harmonic oscillator and the one-loop effective action of scalar QED in a constant field strength-exhibit a natural form of supersymmetric…
We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…
We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a weighted projective space $\mathbb{WCP}_{[n_1,n_2]}^1$, often referred to as a spindle. Starting from the spindle solution of five-dimensional minimal…
We analyze the property of locality with respect to the framework for quantum mechanics based on the path integral formalism. As is well known, this framework makes the same experimental predictions as does the one based on a separable…
We review the derivation of the Atiyah-Singer and Callias index theorems using the recently developed localization method to calculate exactly the relevant supersymmetric path integrals. (Talk given at the III International Conference on…
In this paper, we consider a class of matrix functions, which contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of order $n \ge 2$. We show that every matrix function of this…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
The bundle map $T^*\hspace{-2pt}\operatorname{U}(n)\longrightarrow\operatorname{U}(n)$ provides a real polarization of the cotangent bundle $T^*\hspace{-2pt}\operatorname{U}(n)$, and yields the geometric quantization…
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…