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Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent…
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine Lie algebra and the second one is a new…
We develop a quantum simulator architecture that is suitable for the simulation of $U(1)$ Abelian gauge theories such as quantum electrodynamics. Our approach relies on the ability to control the hopping of a particle through a barrier by…
It is shown that the quaternionic Hilbert space formulation of quantum mechanics allows a quantization, based on a generalized system of imprimitivity, that leads to a description of the motion of a quantum particle in the field of a…
Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces:…
The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in…
Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice…
We quantise the Euclidean torus universe via a combinatorial quantisation formalism based on its formulation as a Chern-Simons gauge theory and on the representation theory of the Drinfel'd double DSU(2). The resulting quantum algebra of…
Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only…
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to…
In this paper we show how to construct explicitly induced representations for bicrossproduct Hopf algebras with abelian kernels starting from one-dimensional characters of the commutative sector. We introduce this technique by means of two…
We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator…
We obtain a characterisation of the Fourier transform on the space of Schwartz-Bruhat functions on locally compact Abelian groups. The result states that any appropriately additive bijection of the Schwartz space onto itself, which…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
This paper shows that quantization of $\pi$-finite spaces, as a functor out of a higher category of spans, is equivariant in two ways: Symmetries of a given polarization/Lagrangian always induce coherent symmetries of the quantization. On…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…