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P. Federbush (1988)
A phase cell approach to Yang–Mills theory. IV: The choice of variablesComm. Math. Phys., 114
Towards a four dimensional Yang – Mills theory
(1986)
Towards a four dimensional Yang–Mills theory, In: M
(2002)
The polynomial ring structure of averaging processes in statistical mechanics, Preprint
T. Bałaban (1984)
Propagators and renormalization transformations for lattice gauge theories. ICommunications in Mathematical Physics, 95
(1987)
Federbush , Towards a four dimensional Yang - Mills theory
T. Bałaban (1985)
Averaging operations for lattice gauge theoriesCommunications in Mathematical Physics, 98
S. Eilenberg, N. Steenrod (1952)
Foundations of Algebraic Topology
P. Federbush (1986)
A phase cell approach to Yang–Mills theory. I: Modes, lattice-continuum dualityComm. Math. Phys., 107
T. Bałaban (1984)
Propagators and renormalization transformations for lattice gauge theories. IICommunications in Mathematical Physics, 96
P. Federbush (1987)
A phase cell approach to Yang–Mills theory. III: Local stability, modified renormalization group transformationComm. Math. Phys., 110
(2002)
The polynomial ring structure of averaging processes in statistical mechanics
P. Federbush (1987)
A phase cell approach to Yang-Mills theoryCommunications in Mathematical Physics, 110
P. Federbush (1987)
Proc. VIIIth International Congress on Mathematical Physics, Marseilles, July 1986
Let S be the set of scalings {n −1:n=1,2,3,...} and let L z =z Z 2, z∈S, be the corresponding set of scaled lattices in R 2. In this paper averaging operators are defined for plaquette functions on L z to plaquette functions on L z′ for all z′, z∈S, z′=dz, d∈{2,3,4,...}, and their coherence is proved. This generalizes the averaging operators introduced by Balaban and Federbush. There are such coherent families of averaging operators for any dimension D=1,2,3,... and not only for D=2. Finally there are uniqueness theorems saying that in a sense, besides a form of straightforward averaging, the weights used are the only ones that give coherent families of averaging operators.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2004
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