Java switch statement: Constant expression required, but it IS constant

So, I am working on this class that has a few static constants:

public abstract class Foo {
    ...
    public static final int BAR;
    public static final int BAZ;
    public static final int BAM;
    ...
}

Then, I would like a way to get a relevant string based on the constant:

public static String lookup(int constant) {
    switch (constant) {
        case Foo.BAR: return "bar";
        case Foo.BAZ: return "baz";
        case Foo.BAM: return "bam";
        default: return "unknown";
    }
}

However, when I compile, I get a constant expression required error on each of the 3 case labels.

I understand that the compiler needs the expression to be known at compile time to compile a switch, but why isn’t Foo.BA_ constant?