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Related papers: Hamiltonians for the quantised Volterra hierarchy

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In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with…

High Energy Physics - Theory · Physics 2015-03-10 Ali H. Chamseddine , Alain Connes , Viatcheslav Mukhanov

Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move…

General Relativity and Quantum Cosmology · Physics 2025-03-12 Naveed Ahmad Shah , S. S. Z. Ashraf , Aasiya Shaikh , Yas Yamin , P. K. Sahoo , Aaqid Bhat , Suhail Ahmad Lone , Mir Faizal , M. A. H. Ahsan

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

Representation Theory · Mathematics 2020-04-21 Samuel A. Lopes , Farrokh Razavinia

We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…

Mathematical Physics · Physics 2026-03-12 Matteo Bruno , Sebastiano Segreto

Noncontextual Pauli Hamiltonians decompose into sets of Pauli terms to which joint values may be assigned without contradiction. We construct a quasi-quantized model for noncontextual Pauli Hamiltonians. Using this model, we give an…

Quantum Physics · Physics 2020-09-28 William M. Kirby , Peter J. Love

The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the…

General Relativity and Quantum Cosmology · Physics 2009-10-28 M. A. Clayton

We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…

Quantum Physics · Physics 2016-04-05 Frantisek Ruzicka

The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…

Quantum Physics · Physics 2019-09-25 David Puertas Centeno , Mariela Portesi

A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom,…

High Energy Physics - Lattice · Physics 2024-11-27 Anthony N. Ciavarella , Christian W. Bauer

A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as…

General Relativity and Quantum Cosmology · Physics 2024-01-11 Mehraveh Nikjoo , Tom Zlosnik

The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The…

High Energy Physics - Theory · Physics 2010-11-01 T. J. Hollowood

We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…

General Relativity and Quantum Cosmology · Physics 2015-06-05 Edward Wilson-Ewing

Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…

Quantum Physics · Physics 2022-03-18 Tamara Kohler , Stephen Piddock , Johannes Bausch , Toby Cubitt

The classification of graded non-alternating Hamiltonian Lie algebras over perfect field of characteristic 2 is obtained. It is shown that the filtered deformations of such algebras correspond to non-alternating Hamiltonian forms with…

Rings and Algebras · Mathematics 2019-01-01 A. V. Kondrateva , M. I. Kuznetsov , N. G. Chebochko

We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the…

General Relativity and Quantum Cosmology · Physics 2020-07-07 Beatriz Elizaga Navascués , Guillermo A. Mena Marugán , Thomas Thiemann

The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…

Quantum Physics · Physics 2019-09-17 Mario Fusco Girard

The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the…

Exactly Solvable and Integrable Systems · Physics 2025-06-11 Orlando Ragnisco , Federico Zullo

We present two maximally superintegrable Hamiltonian systems ${\cal H}_\lambda$ and ${\cal H}_\eta$ that are defined, respectively, on an $N$-dimensional spherically symmetric generalization of the Darboux surface of type III and on an…

A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation…

Quantum Physics · Physics 2021-11-09 Arindam Chakraborty

The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by…

Quantum Physics · Physics 2025-04-07 Federico Rottoli , Colin Rylands , Pasquale Calabrese