Boundary conditions in lattice QFT

Suppose we discretize a scalar field \phi on a finite lattice and
quantize it. How do we set boundary conditions for the discrete field
operators? Specifying \hat\phi_i = 0 breaks the canonical commutation
relations. Do we set the conditions on the expectation values,
<\hat\phi_i> ? What about higher powers of \hat\phi_i ?

--
Roman Werpachowski
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