Branch Point

An argument at which identical points in the Complex Plane are mapped to different points. For example, consider

$$f(z)=z^a.$$

Then $f(e^{0i}) = f(1) = 1$, but $f(e^{2\pi i}) = e^{2\pi i a}$, despite the fact that $e^{i0} = e^{2\pi i}$. Pinch Points are also called branch points.

See also Branch Cut, Pinch Point

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 397-399, 1985.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 391-392 and 399-401, 1953.