Particles and quantum symmetries

Marcinek, Władysław

doi:10.1016/s0034-4877(99)80031-7

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]) This Means That H Is Equipped With a Convolution Inverti1

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2003

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“…Another ingredient of our model is the concept of quantum commutativity [2,19]. Let A be a unital and associative algebra and H be a Hopf algebra.…”

Section: ]) This Means That H Is Equipped With a Convolution Invertimentioning

confidence: 99%

“…This step is connected with the construction of an algebra extension and with a 'decision' which possibility can be realized and which one cannot. The problem how such 'decisions' are made was solved in [19] with the help of quantum commutativity and generalized Pauli exclusion principle. Our approach is based on the previously developed concept of particle systems with generalized statistics and quantum symmetries [15,17,20,22,21,23].…”

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confidence: 99%

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Quantum-classical interactions and galois type extensions

Marcinek

2003

Banach Center Publications

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Abstract. An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle interactions.

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“…Another ingredient of our model is the concept of quantum commutativity [2,19]. Let A be a unital and associative algebra and H be a Hopf algebra.…”

Section: ]) This Means That H Is Equipped With a Convolution Invertimentioning

confidence: 99%

mentioning

confidence: 99%