Related papers: Equivariant and supersymmetric localization in QFT
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…
We show that interval partition functions (transition amplitudes) of three-dimensional $N = 2$ theories admit factorizations into sums of products of hemisphere partition functions with additional normalization factors. We prove the…
Supergeometric Quantum Field Theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without…
In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology…
In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factorizing models)…
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
The main contribution of this paper is a generalization of several previous localization theories in equivariant symplectic geometry, including the classical Atiyah-Bott/Berline-Vergne localization theorem, as well as many cases of the…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
This PhD thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Backlund flow" and polynomial…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
Predicting the 3D structure of proteins is one of the most important problems in current biochemical research. In this article, we explain how to combine recent deep learning advances with the well known technique of quantum walks applied…
Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics. This paper builds on the theory of the…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…
This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…