Supmech: the Geometro-statistical Formalism Underlying Quantum
... underlying QM must be based on a non-commutative algebra of observables. This idea was developed into a scheme of mechanics — called matrix mechanics — by Born, Jordan, Dirac and Heisenberg [34-36]. The proper geometrical framework for the construction of the quantum Poisson brackets of matrix mech ...
... underlying QM must be based on a non-commutative algebra of observables. This idea was developed into a scheme of mechanics — called matrix mechanics — by Born, Jordan, Dirac and Heisenberg [34-36]. The proper geometrical framework for the construction of the quantum Poisson brackets of matrix mech ...
8. Group algebras and Hecke algebras
... By determining which εH (hgi ) εH equal to each other each other we may write out the product as unique linear combination of Hecke basis elements. We summarize this discussion as the following. Proposition 8.5 The Hecke algebra is an associative algebra with basis εH hj εH , in 1-1 correspondence t ...
... By determining which εH (hgi ) εH equal to each other each other we may write out the product as unique linear combination of Hecke basis elements. We summarize this discussion as the following. Proposition 8.5 The Hecke algebra is an associative algebra with basis εH hj εH , in 1-1 correspondence t ...
Oct. 19, 2016 0.1. Topological groups. Let X be a topological space
... (a) for all N1 , N2 in N , there is a N 0 ∈ N such that N 0 ⊂ N1 ∩ N2 . Recall from Milne, Infinite Galois extensions the Proposition 2 (Prop.7.2, first part). We assume in addition X = G is a topological group and x = 1 is the unit element. Then (a) Lemma 1; (b) for all N ∈ N , there is a N 0 ∈ N w ...
... (a) for all N1 , N2 in N , there is a N 0 ∈ N such that N 0 ⊂ N1 ∩ N2 . Recall from Milne, Infinite Galois extensions the Proposition 2 (Prop.7.2, first part). We assume in addition X = G is a topological group and x = 1 is the unit element. Then (a) Lemma 1; (b) for all N ∈ N , there is a N 0 ∈ N w ...
Slide 1
... A system that is rotationally imbalanced will not have its angular momentum and angular velocity vectors in the same direction. A torque is required to keep an unbalanced system rotating. ...
... A system that is rotationally imbalanced will not have its angular momentum and angular velocity vectors in the same direction. A torque is required to keep an unbalanced system rotating. ...
Quantum-like model of unconscious–conscious dynamics
... Chuang, 2000). It seems that the same holds true in mathematical modeling in cognition and psychology (see Asano et al., 2010a,b; Khrennikov, 2010b; Asano et al., 2011, 2012; Khrennikov and Basieva, 2014; Khrennikov et al., 2014), although here the situation is not yet absolutely clear and, obviousl ...
... Chuang, 2000). It seems that the same holds true in mathematical modeling in cognition and psychology (see Asano et al., 2010a,b; Khrennikov, 2010b; Asano et al., 2011, 2012; Khrennikov and Basieva, 2014; Khrennikov et al., 2014), although here the situation is not yet absolutely clear and, obviousl ...
Quantum algebras and parity-dependent spectra
... may be represented in terms of operators obeying certain commutation relations. In this paper we explore a new way of expressing the generators of SU(1,1). There is a system of commutation relations which generalizes the standard commutation relations of the simple harmonic oscillator. The generator ...
... may be represented in terms of operators obeying certain commutation relations. In this paper we explore a new way of expressing the generators of SU(1,1). There is a system of commutation relations which generalizes the standard commutation relations of the simple harmonic oscillator. The generator ...