4 Matching Annotations
 Feb 2023

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 physics/mathematics  Classical Physics  Quantum Mechanics <br /> <br />  State Space  fields satisfying equations of laws<br> the state is given by a point in the space  vector in a complex vector space with a Hermitian inner product (wavefunctions) <br />  Observables  functions of fields<br> usually differential equations with realvalued solutions  selfadjoint linear operators on the state space<br> some confusion may result when operators don't commute; there are usually no simple (realvalued) numerical solutions 



Principle (Observables). States for which the value of an observable can becharacterized by a welldefined number are the states that are eigenvectors forthe corresponding selfadjoint operator. The value of the observable in such astate will be a real number, the eigenvalue of the operator.
What does he mean precisely by "principle"?

 Jun 2018

arxiv.org arxiv.org

Remark1.73.IfPandQare total orders andf:P!Qand1:Q!Pare drawn witharrows bending as in Exercise 1.72, we believe thatfis left adjoint to1iff the arrows donot cross. But we have not proved this, mainly because it is difficult to state precisely,and the total order case is not particularly general

The preservation of meets and joins, and hence whether a monotone map sustainsgenerative effects, is tightly related to the concept of a Galois connection, or moregenerally an adjunction.
