Related papers: Completing the Bootstrap Program for $\mathrm{T}\b…
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…
Two distinct $\eta$-deformations of strings on AdS$_5\times$S$^5$ can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare…
We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their…
In the framework of the algebraic approach to form factors in two-dimensional integrable models of quantum field theory we consider the reduction of the sine-Gordon model to the $\Phi_{13}$-perturbation of minimal conformal models of the…
In this thesis, we investigate properties of the one-parameter $\beta$- and the three-parameter $\gamma_i$-deformed descendents of $\mathcal{N}=4$ SYM theory. We find additional multi-trace interactions that must be included in the deformed…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is…
We consider the general properties of effective field theories. We note that the freedom to fix the renormalization conditions in the effective field theory is not as great as it seems. The consideration of minimal requirements of…
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial…
Deformations of many-body Hamiltonians by certain products of conserved currents, referred to as $T\bar{T}$-deformations, are known to preserve integrability. Generalised $T\bar{T}$-deformations, based on the complete space of pseudolocal…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In…
We discuss the role of formal deformation theory in quantum field theories and present various ``higher operations'' which control their deformations, (generalized) OPEs, and anomalies. Particular attention is paid to…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
Electromagnetic scattering and absorption by material particles is a fundamental physical problem with a broad range of applications, going from laboratory experiments, biology and material sciences, all the way up to environmental studies…
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A solid-state quantum emitter is one of the indispensable components for optical quantum technologies. Ideally, an emitter should have a compatible wavelength for efficient coupling to other components in a quantum network. It is therefore…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
The decomposition of arbitrary unitary transformations into sequences of simpler, physically realizable operations is a foundational problem in quantum information science, quantum control, and linear optics. We establish a 1D Quantum Field…