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- W2117018681 abstract "In this paper we shall re-visit the well-known Schrodinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general, underlying dynamical process. In both cases we shall see that the evolution of a quantum state $P_psi=varrho(0)$ has the not so well-known pseudo-quadratic form $partial_tvarrho(t)=mathbf{V}^starvarrho(t)mathbf{V}$ where $mathbf{V}$ is a vector operator in a complex Minkowski space and the pseudo-adjoint $mathbf{V}^star$ is induced by the Minkowski metric $boldsymbol{eta}$. The interesting thing about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the emph{Belavkin Formalism}; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be `unraveled' in a second-quantized Minkowski space. Working in such a space provided the author with the means to construct a QS (quantum stochastic) Duhamel principle and known applications to a Schrodinger dynamics perturbed by a continual measurement process are considered. What is not known, but presented here, is the role of the Lorentz transform in quantum measurement, and the appearance of Riemannian geometry in quantum measurement is also discussed." @default.
- W2117018681 created "2016-06-24" @default.
- W2117018681 creator A5010409671 @default.
- W2117018681 date "2014-07-10" @default.
- W2117018681 modified "2023-09-27" @default.
- W2117018681 title "Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle" @default.
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