Electronic Resource
Springer
Communications in mathematical physics
16 (1970), S. 157-183
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We consider a self-interacting scalar boson field in two-dimensional space-time with self-interaction given by an arbitrary Wick polynomial of even degree in the field. It is shown that the field theory can be constructed in a Hilbert space of physical states. The hamiltonian is a positive self-adjoint operator possessing a physical vacuum. The method of proof consists of imposing and then removing three cutoffs: a box cutoff, an ultraviolet cutoff, and a space cutoff. As the first two are removed the resolvents of the cutoff hamiltonians converge uniformly and this leads to the self-adjointness of the spatially cutoff hamiltonian.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01646785
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