Quantum mechanics in 1 + 1 dimensions is equivalent to qft in 0 + 1 dimensions. This is because the position [itex] x(t) [/itex] of a particle can be replaced by a scalar field [itex] \phi(t) [/itex], and the momentum is replaced by the momentum conjugate of [itex] \phi(t) [/itex]. Also, in the bosonic construction of heterotic string theory, the left moving bosons can be combined with the right moving ones to make out the coordinates of spacetime. Does it mean that spacetime dimensions can be interpreted as bosonic fields, with an associated bosonic particle? I know it's probably not the case so I'd like to know where the equivalence breaks down.