  One-dimensional quantum systems admit duality relations that put hard core
spinless bosons and fermions in one-to-one correspondence via Girardeau's
mapping theorem. The simplest models of soft bosons interacting via zero-range
potentials can also be mapped onto dual interacting fermions. However, a
systematic approach to one-dimensional statistical transmutation for arbitrary
low-energy interactions in the spinless and spinful or multicomponent cases has
remained elusive. I develop a general theory of local unitary transformations
between one-dimensional quantum systems of bosons and fermions with arbitrary
spin or internal structure, single-particle dispersion -- including
non-relativistic, relativistic or otherwise -- and low-energy interactions in
the universal regime. These transformations generate families of new duality
relations and models that relate the strong and weak coupling limits of the
respective dual theories.
