From Classical Mechanics to Quantum Field Theory
128 From Classical Mechanics to Quantum Field Theory. A Tutorial elementary property of the physical system,μ(E) denotes the pro ...
Mathematical Foundations of Quantum Mechanics 129 For future convenience, we observe that our model ofclassicalelementary prop- ...
130 From Classical Mechanics to Quantum Field Theory. A Tutorial Definition 2.3.5.IfX,Y are lattices, a maph:X→Y is a(lattice) h ...
Mathematical Foundations of Quantum Mechanics 131 2.3.2 The non-Boolean logic of QM, the reason why observables are selfadjoint ...
132 From Classical Mechanics to Quantum Field Theory. A Tutorial The converse implication is obvious. As preannounced, it turns ...
Mathematical Foundations of Quantum Mechanics 133 Proof. L 0 includes both 0 andIbecauseL 0 is maximally commutative. Having (i) ...
134 From Classical Mechanics to Quantum Field Theory. A Tutorial We are in a position to clarify why, in this context, observabl ...
Mathematical Foundations of Quantum Mechanics 135 P∈L(H)\{ 0 }there exists an atomAwithA≤P (L(H)is then called atomic); For ever ...
136 From Classical Mechanics to Quantum Field Theory. A Tutorial P∧Qfor everyP,Q. There are several proposals, very different in ...
Mathematical Foundations of Quantum Mechanics 137 Sol`er^13 , Holland^14 and Aerts–van Steirteghem^15 have found sufficient hypo ...
138 From Classical Mechanics to Quantum Field Theory. A Tutorial Remark 2.3.16. Notice that, above,T†T is selfadjoint andσ(T†T)∈ ...
Mathematical Foundations of Quantum Mechanics 139 if at least one of the Tk belongs to B 1 (H), the remaining ones are in B(H),a ...
140 From Classical Mechanics to Quantum Field Theory. A Tutorial of|T|(it exists for the previous theorem since|T|is trace class ...
Mathematical Foundations of Quantum Mechanics 141 the sum on the left-hand side being computed with respect to the strong operat ...
142 From Classical Mechanics to Quantum Field Theory. A Tutorial Proposition 2.3.23.LetHbe a complex Hilbert space and letT∈B 1 ...
Mathematical Foundations of Quantum Mechanics 143 Theorem 2.3.26(Bell-Kochen-Specker theorem). LetHbe a complex Hilbert space of ...
144 From Classical Mechanics to Quantum Field Theory. A Tutorial whereNis an eigenvector basis forρ,pφ∈[0,1]for anyφ∈N,and ∑ φ∈N ...
Mathematical Foundations of Quantum Mechanics 145 Notice|〈φ, ψ〉|^2 =|〈ψ,φ〉|^2 , so the probability transition of the state deter ...
146 From Classical Mechanics to Quantum Field Theory. A Tutorial (b) Measuring instruments are commonly employed toprepare a sys ...
Mathematical Foundations of Quantum Mechanics 147 2.3.5 von Neumann algebra of observables, superselection rules The aim of this ...
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