Infinitesimal Canonical Transformation

[Leb]

Hi all!

Another questions which is due to the gaps in my calculus knowledge.

In these notes: http://people.hofstra.edu/Gregory_C_Levine/qft.pdf in the line above eq. (1) where it says that notation [itex]P[/itex] is now unecessary, is it because [itex]\partial{ (p+\delta p)} [/itex] is much smaller than [itex]p+\delta p[/itex] and most of the change will only happen in [itex]p[/itex] and hence the use of only [itex]\partial {p}[/itex] ?



I wish someone could explain the usage of these [itex]\delta x[/itex] and [itex]\partial {x}[/itex] when all of this "just the notation" argument is used... But I suppose this is too broad.

 

[lippyka]

Yes, the main reason for the use of \partial {p} instead of P is that the change in the variable will be mainly due to the change in p, hence it is sufficient to use only the partial derivative of p. The notation \delta x and \partial {x} are used to represent the change in a variable x, where \delta x is the difference between two values of x (for example, the difference between the initial and final values) and \partial {x} is the derivative of x with respect to some other variable (like time).