windows username: shortcut for current machine?

Some applications insist that you write a username like domain\user, even if the current computer is not in a domain.

Is there a shortcut that resolves to domain to the current machine?

I mean something similar like these shortcuts:

• . for SQL Serve (.\Northwind resolves to the Northwind database on the current computer)
• http://localhost/index.html which resolves to index.html over http on the current machine.

Even better: is there a shortcut that points to the current user?