Results 1 to 10 of about 14,701 (175)
Non-Commutative Worlds and Classical Constraints [PDF]
Entropy, 2018 This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators.
Louis H. Kauffman
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Relative unitary commutator calculus, and applications
Journal of Algebra, 2011 This note revisits localisation and patching method in the setting of generalised unitary groups. Introducing certain subgroups of relative elementary unitary groups, we develop relative versions of the conjugation calculus and the commutator calculus in unitary groups, which are both more general, and substantially easier than the ones available in ...
Hazrat, Roozbeh (R16959) +2 more
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Relative commutator calculus in Chevalley groups
Journal of Algebra, 2013 We revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the conjugation calculus and the commutator calculus in Chevalley groups $G( ,R)$, $\rk( )\geq 2$, which are both more general, and substantially easier than the ones ...
Hazrat, Roozbeh (R16959) +2 more
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Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation [PDF]
Quantum, 2022 We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators.
Dong An, Di Fang, Lin Lin
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Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices
Comptes Rendus. Mathématique, 2023 We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac{1}{2}\Delta + \frac{1}{2}|x|^{2} $ acting on $L^{2}(\mathbb{R}^{d ...
van Neerven, Jan +2 more
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Non-commutative functional calculus: Unbounded operators [PDF]
Journal of Geometry and Physics, 2009 In a recent work, \cite{cgss}, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from \cite{cgss} can be extended to the unbounded case, and we highlight the crucial differences between the two cases.
Sabadini, Irene +11 more
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Quasi-shuffle Algebras in Non-commutative Stochastic Calculus [PDF]
, 2021 This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of It{\^o} calculus for matrix-valued semimartin-gales. Its aim is to unfold in detail the algebraic structures implied for iterated It{\^o} and Stratonovich integrals. These constructions generalise the classical rules of Chen calculus for
Ebrahimi-Fard, Kurusch +1 more
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, 2011 In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and enhanced versions of
Hazrat, R. +3 more
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Generating q-Commutator Identities and the q-BCH Formula
Advances in Mathematical Physics, 2016 Motivated by the physical applications of q-calculus and of q-deformations, the aim of this paper is twofold. Firstly, we prove the q-deformed analogue of the celebrated theorem by Baker, Campbell, and Hausdorff for the product of two exponentials.
Andrea Bonfiglioli, Jacob Katriel
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Noncommutative integration calculus [PDF]
Journal of Mathematical Physics, 1995 A noncommutative integration calculus arising in the mathematical description of Schwinger terms of fermion–Yang–Mills systems is discussed. The differential complexes of forms u0[ε,u1]...[ε,un] with ε a grading operator on a Hilbert space ℋ and ui bounded operators on ℋ which naturally contains the compactly supported de Rham forms on Rd (i.e., ε is ...
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