Related papers: On the quantization of continuous non-ultralocal i…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the…
We consider a general anisotropic massive SU(N) fermionic model, and investigate its quantum integrability. In particular, by regularizing singular operator products, we derive a system of equations resulting in the S-matrix and find some…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
A scheme suitable for describing quantum nonultralocal models including supersymmetric ones is proposed. Braided algebras are generalised to be used through Baxterisation for constructing braided quantum Yang--Baxter equations.…
In this paper we develop flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with an $\ell_2$ fit-to-data term and an $\ell_p$ penalization term, for $p\geq 1$. First we approximate…
The Batalin-Vilkovisky formalism is applied to quantise the ${\cal N}=1$ supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindstr\"om and Ro\v{c}ek in 1983 in Minkowski superspace and is lifted to a…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
Acin et al. introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
We explain the effective renormalization method of quantum field theory in the Batalin-Vilkovisky formalism and illustrate its mathematical applications by three geometric examples: (1) Topological quantum mechanics and algebraic index, (2)…
On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field…
Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultra-violet regularisation scheme for loop integrals in quantum field theory which we call $\eta$ regularisation. This allows us to reveal a…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli-Villars fields. Unphysical…
We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior,…
In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of…
The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use…
Indefinite causal structure is generically present in theories of quantum gravity admitting a path integral formulation. We show that summing over causal structures eliminates ultraviolet divergences of matter QFT and resolves spacetime…