Related papers: Geometric Complexity Theory VII: Nonstandard quant…
In this article the study of the Prime Graph Question for the integral group ring of almost simple groups which have an order divisible by exactly $4$ different primes is continued. We provide more details on the recently developed "lattice…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
We semiclassicalise the standard notion of differential calculus in noncommutative geometry on algebras and quantum groups. We show in the symplectic case that the infinitesimal data for a differential calculus is a symplectic connection,…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups $B_u(Q)$ for…
Using the curved bc-beta-gamma system (a tensor product of a Heisenberg and a Clifford vertex algebra) we introduce quantum analogy of Lichnerowicz differential. As follows we suggest new machinery for finding the Lichnerowicz-Poisson…
We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the…
We review seven models, which consistently couple quantum matter and (Newtonian) gravity in a non standard way. For each of them we present the underlying motivations, the main equations and, when available, a comparison with experimental…
The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and…
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…
We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
In this paper we extend the algorithm for extraspecial groups in \cite{iss07}, and show that the hidden subgroup problem in nil-2 groups, that is in groups of nilpotency class at most 2, can be solved efficiently by a quantum procedure. The…
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question,…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…
In this paper, the Lie group $G_{NC}^{\alpha,\beta,\gamma}$, of which the kinematical symmetry group $G_{NC}$ of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero $\alpha$, $\beta$ and $\gamma$, is…
In this paper, we give an explicit combinatorial realization of the crystal B(\lambda) for an irreducible highest weight U_q(q(n))-module V(\lambda) in terms of semistandard decomposition tableaux. We present an insertion scheme for…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…