Finite size effect

introduction

Casimir effect in QED is one example of finite size effect
the stress on the bounding surfaces when quantum field is confined to finite volume of space
type of boundaries
- real material media
- interface between two different phases of the vacuum of a field theory such as QCD, in which case colored field may only exist in the interior region
- topology of space
the boundaries restrict the modes of the quantum fields
give rise to measurable and important forces

zero-point energy in the presence of the boundaries
- sum over all modes
- any kind of constraint or boudary conditions on the the zero-point modes of the quantum fields in question, including backgrounds such as gravity
- In a model without boundary conditions, the Hamiltonian value associated wih the vacuum or ground state, called zero-point energy, is usually discarded because, despite being infinite, may be reabsorbed in a suitable redefinition of the energy origin
- there are several ways to put such an adjustment into practice, normal ordering being oneof the most popular
Green's functions method
- represents the vacuum expectation value of the produc of fields