Related papers: Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes

Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes

URL: http://arxiv.org/abs/2103.06666v3
Date: Thu, 6 Jan 2022 18:11:05 GMT
Title: Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
Authors: Meer Ashwinkumar, Lennart Schmidt, Meng-Chwan Tan
Abstract summary: We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. We approximate the corresponding classical Nambu brackets using $mathfraksl(Nlceilfracn2rceil,mathbbC)$-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product.
Score: 0.5156484100374059
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. That is, we approximate the corresponding classical Nambu brackets using $\mathfrak{sl}(N^{\lceil\frac{n}{2}\rceil},\mathbb{C})$-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the $N\rightarrow \infty$ limit. We then apply this approximation to the super $4$-brane in $9$ dimensions and give a regularized action in analogy with the matrix quantization of the supermembrane. This action exhibits a reduced gauge symmetry that we discuss from the viewpoint of $L_\infty$-algebras in a slight generalization to the construction of Lie $2$-algebras from Bagger--Lambert $3$-algebras.

Related papers

Limit formulas for norms of tensor power operators [49.1574468325115]
Given an operator $phi:Xrightarrow Y$ between Banach spaces, we consider its tensor powers. We show that after taking the $k$th root, the operator norm of $phiotimes k$ converges to the $2$-dominated norm.
arXiv Detail & Related papers (2024-10-30T14:39:21Z)
The Communication Complexity of Approximating Matrix Rank [50.6867896228563]
We show that this problem has randomized communication complexity $Omega(frac1kcdot n2log|mathbbF|)$. As an application, we obtain an $Omega(frac1kcdot n2log|mathbbF|)$ space lower bound for any streaming algorithm with $k$ passes.
arXiv Detail & Related papers (2024-10-26T06:21:42Z)
Polyadic supersymmetry [0.0]
We introduce a polyadic analog of supersymmetry by considering the polyadization procedure applied to the toy model of one-dimensional supersymmetric quantum mechanics. We find new brackets with a reduced arity of $2leq mn$ and a related series of $m$-ary superalgebras.
arXiv Detail & Related papers (2024-06-04T10:33:29Z)
Volichenko-type metasymmetry of braided Majorana qubits [0.0]
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits. Mixed-bracket Heisenberg-Lie algebras are introduced.
arXiv Detail & Related papers (2024-06-02T21:50:29Z)
Quantum charges of harmonic oscillators [55.2480439325792]
We show that the energy eigenfunctions $psi_n$ with $nge 1$ are complex coordinates on orbifolds $mathbbR2/mathbbZ_n$. We also discuss "antioscillators" with opposite quantum charges and the same positive energy.
arXiv Detail & Related papers (2024-04-02T09:16:18Z)
Polyadic sigma matrices [0.0]
We generalize $sigma$-matrices to higher arities using the polyadization procedure proposed by the author. The presentation of $n$-ary $SUleft( 2right) $ in terms of full $Sigma$-matrices is done using the Hadamard product.
arXiv Detail & Related papers (2024-03-28T12:19:46Z)
Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model [77.34726150561087]
We provide a systematic treatment of boundaries based on subgroups $Ksubseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $Xisubseteq D(G)$ and we explicate its structure as a strong $*$-quasi-Hopf algebra. As an application of our treatment, we study patches with boundaries based on $K=G$ horizontally and $K=e$ vertically and show how these could be used in a quantum computer
arXiv Detail & Related papers (2022-08-12T15:05:07Z)
Quantum teleportation in the commuting operator framework [63.69764116066747]
We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
arXiv Detail & Related papers (2022-08-02T00:20:46Z)
First quantization of braided Majorana fermions [0.0]
A $mathbb Z$-graded qubit represents an even (bosonic) "vacuum state" Multiparticle sectors of $N$, braided, indistinguishable Majorana fermions are constructed via first quantization.
arXiv Detail & Related papers (2022-03-03T15:43:38Z)
Quantum double aspects of surface code models [77.34726150561087]
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
arXiv Detail & Related papers (2021-06-25T17:03:38Z)
$C^*$-fermi systems and detailed balance [0.0]
A systematic theory of product and diagonal states is developed for tensor products of $mathbb Z$-graded $*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice.
arXiv Detail & Related papers (2020-10-14T15:16:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.