From Classical Mechanics to Quantum Field Theory
48 From Classical Mechanics to Quantum Field Theory. A Tutorial AWeyl systemis a map: W:S→U(H) z→̂W(z), (1.230) withŴ(z)Ŵ†(z) ...
A Short Course on Quantum Mechanics and Methods of Quantization 49 By Stone’s theorem[ 34 ], there exists an essentially self-ad ...
50 From Classical Mechanics to Quantum Field Theory. A Tutorial Thus, one has: ̂W(q,p)=Û(q)V̂(p)exp{−ıqp/} (1.249) or explicit ...
A Short Course on Quantum Mechanics and Methods of Quantization 51 Thanks to the Von Neumann’s theorem[ 34 ], we can affirm then ...
52 From Classical Mechanics to Quantum Field Theory. A Tutorial whichissuchthat: F†Q̂F=−P,̂ F†P̂F=Q.̂ (1.263) It is simple to ve ...
A Short Course on Quantum Mechanics and Methods of Quantization 53 and is such that: ŴT(z+z′)=̂WT(z)̂WT(z′)exp{−ıωT(z,z′)/ 2 } ...
54 From Classical Mechanics to Quantum Field Theory. A Tutorial As usual, we can define a one-parameter family of unitary operat ...
A Short Course on Quantum Mechanics and Methods of Quantization 55 Proceeding just as in the previous example, we obtain: ̂Wt(q, ...
56 From Classical Mechanics to Quantum Field Theory. A Tutorial gives a map Ω from the space of functionsF ( R^2 ) to operatorsO ...
A Short Course on Quantum Mechanics and Methods of Quantization 57 Using then the identity:Fs(qnpm)(η,ξ)=2π(−1)mın+mδ(n)(η)δ(m)( ...
58 From Classical Mechanics to Quantum Field Theory. A Tutorial Using Eq. (1.254), we have: Tr [ Ŵ(x, k)̂W†(ξ,η) ] =2πδ(x−ξ)δ( ...
A Short Course on Quantum Mechanics and Methods of Quantization 59 (2) Setting:Ô=Q̂, we find at once: Ω−^1 ( Q̂ ) (q,p)=q. (1.3 ...
60 From Classical Mechanics to Quantum Field Theory. A Tutorial as well as ∫ dqdp 2 π f(q,p) = Tr [Ω (f]). (1.317) This allows ...
A Short Course on Quantum Mechanics and Methods of Quantization 61 1.3.3.5 The Moyal product and the quantum to classical transi ...
62 From Classical Mechanics to Quantum Field Theory. A Tutorial The latter form exhibits explicitly the Moyal product as a serie ...
A Short Course on Quantum Mechanics and Methods of Quantization 63 (4) Iff=qandg=p(or vice versa), one obtains: (q∗p)(q,p)=qp+ ı ...
64 From Classical Mechanics to Quantum Field Theory. A Tutorial Unlessfand/orgare at most quadratic,{f,g}∗={f,g}. Therefore, th ...
A Short Course on Quantum Mechanics and Methods of Quantization 65 [20] J. Glimm, A. Jaffe,Quantum physics. A functional integra ...
This page intentionally left blankThis page intentionally left blank ...
Chapter 2 Mathematical Foundations of Quantum Mechanics: An Advanced Short Course Valter Moretti Department of Mathematics of th ...
«
1
2
3
4
5
6
7
8
9
10
»
Free download pdf