  A reformulation of a physical theory in which measurements at the initial and
final moments of time are treated independently is discussed, both on the
classical and quantum levels. Methods of the standard quantum mechanics are
used to quantize boundary phase space to obtain boundary quantum mechanics -- a
theory that does not depend on the distinction between the initial and final
moments of time, a theory that can be formulated without reference to the
causal structure. As a supplementary material, the geometrical description of
quantization of a general (e.g. curved) configuration space is presented.
