Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-11-10
Phys.Rev. D48 (1993) 4919-4923
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, 2 figures, plain TEX
Scientific paper
10.1103/PhysRevD.48.4919
A recently-proposed technique, called the dimensional expansion, uses the space-time dimension $D$ as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine the Ising limit of a self-interacting scalar field theory. We compute the first few coefficients in the dimensional expansion for $\gamma_{2n}$, the renormalized $2n$-point Green's function at zero momentum, for $n\!=\!2$, 3, 4, and 5. Because the exact results for $\gamma_{2n}$ are known at $D\!=\!1$ we can compare the predictions of the dimensional expansion at this value of $D$. We find typical errors of less than $5\%$. The radius of convergence of the dimensional expansion for $\gamma_{2n}$ appears to be ${{2n}\over {n-1}}$. As a function of the space-time dimension $D$, $\gamma_{2n}$ appears to rise monotonically with increasing $D$ and we conjecture that it becomes infinite at $D\!=\!{{2n}\over {n-1}}$. We presume that for values of $D$ greater than this critical value, $\gamma_{2n}$ vanishes identically because the corresponding $\phi^{2n}$ scalar quantum field theory is free for $D\!>\!{{2n}\over{n-1}}$.
Bender Carl M.
Boettcher Stefan
No associations
LandOfFree
Dimensional Expansion for the Ising Limit of Quantum Field Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dimensional Expansion for the Ising Limit of Quantum Field Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimensional Expansion for the Ising Limit of Quantum Field Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337224