Question: Spring AOP depends on proxy mechanism - J2SE dynamic proxies or using CGLIB(according to the spring documentation). 
Is it possible to use the AOP mechanism defined by Spring without creating/declaring the beans in the spring application context?

If its not possible with Spring - is AspectJ's Load time Weaving(LTW) or Compile Time Weaving (CTW) would help resolve the issue?

Requirement : Trying to implement logging and transaction management for a old project of mine without declaring the POJO's as spring beans.

Answer: 
No, you have to put them under Spring's control. You can't ask Spring to advise beans that it doesn't know about.

No calls to "new"; have to replace those with application context.
As stated by @duffymo Spring can only operate on beans declared within its context. 

AspectJ, both LTW and CTW, can be used to achieve what you want.

Another tools you might consider is [Byteman](https://www.jboss.org/byteman.html), which operate at a lower level but has also a lower overhead if performance is an issue for you.