Related papers: On the Quantization of Nambu Brackets
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
We propose an extension of n-ary Nambu-Poisson bracket to superspace R^{n|m} and construct by means of superdeterminant a family of Nambu-Poisson algebras of even degree functions, where the parameter of this family is an invertible…
We present an implementation of the three-neutron quantization condition (QC) derived in previous work. We construct the matrices appearing in the QC and determine solutions numerically. The symmetries of the QC allow the projection onto…
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under…
The Grassmann-odd Nambu-like bracket corresponding to an arbitrary Lie algebra and realized on the Grassmann algebra is proposed.
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
We enhance the tribracket counting invariant with \textit{tribracket brackets}, skein invariants of tribracket-colored oriented knots and links analogously to biquandle brackets. This infinite family of invariants includes the classical…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
In his pioneering paper [Phys. Rev. E 7, 2405 (1973)], Nambu proposed the idea of multiple Hamiltonian systems. The explicit example examined there is equivalent to the so(3) Lie-Poisson system, which represents noncanonical Hamiltonian…
A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu--Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step…
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they…
We establish a connection between 4-rebits (real qubits) and the Nambu-Goto action with target `spacetime' of four time and four space dimensions ((4+4)-dimensions)). We motivate the subject with three observations. The first one is that a…
Automorphism, isomorphism, and embedding problems are investigated for a family of Nambu-Poisson algebras (or $n$-Lie Poisson algebras) using Poisson valuations.
Inspired by geometric engineering method, we approach qubit systems in the context of D-branes in type II superstrings. Concretely, we establish a correspondence between such quantum systems and polyvalent singularities appearing in local…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…