547 research outputs found
The Renormalization Group According to Balaban - III. Convergence
This is an expository account of Balaban's approach to the renormalization
group. The method is illustrated with a treatment of the ultraviolet problem
for the scalar phi^4 model on a toroidal lattice in dimension d=3. In this
third paper we demonstrate convergence of the expansion and complete the proof
of a stability bound.Comment: 37 page
The Renormalization Group According to Balaban - I. Small fields
This is an expository account of Balaban's approach to the renormalization
group. The method is illustrated with a treatment of the the ultraviolet
problem for the scalar phi^4 model on a toroidal lattice in dimension d=3. This
yields another proof of the stability bound. In this first paper we analyze the
small field contribution to the partition function.Comment: 52 pages. Some corrections, additions, reorganizatio
The Dirac Sea
We give an alternate definition of the free Dirac field featuring an explicit
construction of the Dirac sea. The treatment employs a semi-infinite wedge
product of Hilbert spaces. We also show that the construction is equivalent to
the standard Fock space construction.Comment: 7 page
Sine-Gordon Revisited
We study the sine-Gordon model in two dimensional space time in two different
domains. For beta > 8 pi and weak coupling, we introduce an ultraviolet cutoff
and study the infrared behavior. A renormalization group analysis shows that
the model is asymptotically free in the infrared. For beta < 8 pi and weak
coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A
renormalization group analysis shows that the model is asymptotically free in
the ultraviolet.Comment: 43 pages, Latex 2.0
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