Non-Compact Pure Gauge QED in 3D is Free

Abstract

For all Poincaré invariant Lagrangians of the form $\mathcal{L}\equiv f(F_{\mu \nu })$, in three Euclidean dimensions, where $f$ is any invariant function of a non-compact $U(1)$ field strength $F_{\mu \nu }$, we find that the only continuum limit (described by just such a gauge field) is that of free field theory: First we approximate a gauge invariant version of Wilson's renormalization group by neglecting all higher derivative terms $\sim {\partial }^{n}F$ in $\mathcal{L}$, but allowing for a general non-vanishing anomalous dimension. Then we prove analytically that the resulting flow equation has only one acceptable fixed point: the Gaussian fixed point. The possible relevance to high-$T_c$ superconductivity is briefly discussed.

11 pages, plain tex, uses harvmac. Minor additions - version to be published in Physics Letters B

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Cited by in corpus (25)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Exact Renormalization Group Equations. An Introductory Review
• Fundamentals of the Exact Renormalization Group
• Asymptotic safety in the f(R) approximation
• A gauge invariant exact renormalization group I
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• Large N and the renormalization group
• A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
• Asymptotic solutions in asymptotic safety
• A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Properties of derivative expansion approximations to the renormalization group
• Triviality from the Exact Renormalization Group
• BRST in the Exact RG
• C Function Representation of the Local Potential Approximation
• Exact renormalization group study of fermionic theories
• Background independent exact renormalisation
• Provable properties of asymptotic safety in $f(R)$ approximation
• General Computations Without Fixing the Gauge
• Functional flows in QED and the modified Ward-Takahashi identity
• Conformal anomaly from gauge fields without gauge fixing
• Two Phases for Compact U(1) Pure Gauge Theory in Three Dimensions
• Exact renormalization group approach in scalar and fermionic theories