The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories

Abstract

We classify the physical observables in spontaneously broken nonlinearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical nonlinearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.

20 pages, 1 figure

References in corpus (4)

• Ultraviolet Complete Electroweak Model Without a Higgs Particle
• A Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group
• Further Comments on the Symmetric Subtraction of the Nonlinear Sigma Model
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Cited by in corpus (2)

• Renormalization Group Equation for Weakly Power Counting Renormalizable Theories
• Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach