According to Hartl & Clark on population genetics:
"Population genetics deals with Mendel's laws and other genetic
principles as they apply to entire populations of organisms.... also
includes the study of the various forces that result in evolutionary
changes in species through time."
According to Conner & Hartl also on population genetics:
"Population genetics is the study of naturally occurring genetic
differences between organisms; these differences are called genetic
variation. Genetic variation is important because it is the raw
material for evolution... to understand the purview of population
genetics, we need to have a better understanding of populations and
According to Conner & Hartl on quantitative genetics:
"Most phenotypic traits do not fall in to distinct categories, but
rather are continuously distributed... These traits are called
quantitative or metric traits because they need to be measured not
According to Falconer & Mackay on quantitative genetics (my personal favourite book on quant gen, which spends the first 5 chapters going through population genetics):
"Quantitative genetics is concerned with the inheritance of those
differences between individuals that of degree rather than of kind,
quantitative rather than qualitative.... It is nevertheless a basic
premise of quantitative genetics that the inheritance of quantitative
differences depends on genes subject to the same laws of transmission
and having the same general properties as the genes whose transmission
and properties are displayed by qualitative differences.
Quantitative genetics is therefore an extension of Mendelian genetics, resting squarely on Mendelian principles as its
Personally I would say that evolution is inescapably a population genetics process and (virtually) no study of it can be done without some understanding of population genetic principles. Many evolutionary genetics problems can be best dealt with using quantitative methods, and quantitative genetics is an extension of population genetic principles. Population genetics relies on selection, drift, mutation and gene flow - these are all key quantitative genetics.
Population genetics study focuses then on the four basic principles above from a (simplified) Mendelian view, while quantitative genetics deals with more realistic evolutionary genetic phenomena by allowing for, and assessing, genetic variance from many loci influenced by additivity, dominance, and environmental factors. Both fields are studies of evolutionary genetics, population genetics can be studied whilst ignoring quantitative genetics, but quantitative genetics relies on population genetics principles so I would call it an extension of - but not sub-field - of population genetics.