A partial elucidation of the gauge principle

Abstract

The elucidation of the gauge principle "is the most pressing problem in current philosophy of physics" Michael Redhead in 2003. This paper argues for two points that contribute to this elucidation in the context of Yang-Mills theories. 1) Yang-Mills theories, including quantum electrodynamics, form a class. They should be interpreted together. To focus on electrodynamics is potentially misleading. 2) The essential role of gauge and BRST symmetries is to provide a local field theory that can be quantized and would be equivalent to the quantization of the non-local reduced theory. If this is correct, the gauge symmetry is significant, not so much because it implies ontological consequences, but because it allows us to quantize theories that we would not be able to quantize otherwise. Thus, in the context of Yang-Mills theories, it is essentially a pragmatic principle. This does not seem to be the case for the gauge symmetry in general relativity.

Artificial versus Substantial Gauge Symmetries: A Criterion and an Application to the Electroweak Model

“…This is directly relevant to our discussion of the electroweak model in the next section. 11 As an aside, notice that in line with the general remark in section 2.1 following Eq. (3), Γ is not in the gauge orbit of A and they should not be seen as related by a mere gauge transformation, as indeed the tetrad e is not an element of the Lorentz gauge group SO.…”

“…The gauge structure of General Relativity is most apparent in the tetrad formulation. It is based on the bundle of pseudo-orthonormal frames with the Lorentz group as structure group, P(M, S O(1, 3)), endowed with the spin connection A ∈ Λ 1 (M, so(1, 3)) whose curvature is the Riemann 2-form By inspection, it appears clearly that the tetrad field e = e a µ is a local dressing field since it satisfies e γ = γ −1 e. The SO-invariant local composite fields are none other than the linear connection Γ = e −1 Ae + e −1 de, and its Riemann curvature R(Γ) = e −1 R(A)e. 11 The Lorentz gauge symmetry is then artificial and can be erased at no cost in the theory, whose Lagrangian reduces to the standard Einstein-Hilbert metric formulation: L(θ, A) = L EH (g, Γ). The metric field, written as g = e T ηe, indeed appears as a natural SO-invariant field in the Lagrangian.…”

“…It is closely related to (3) Separability: Physical properties (fields configurations) of any region of spacetime are recovered from physical properties of its constitutive subregions. Relativistic causality is still non-negotiable, so failure of locality means infringing field locality [12] or separability [13; 14], or both [11]. 2 One recalls the notorious example of [19], or the controversial interview by Lawrence Krauss in The Atlantic [20] where he opinioned that "[...] the worst part of philosophy is the philosophy of science; the only people, as far as I can tell, that read work by philosophers of science are other philosophers of science.…”

The construction of the Higgs mechanism and the emergence of the electroweak theory

“…15 Glashow 1961. 16 Philosophical discussions of this concept can be found in Lyre 2001, Martin 2002, Healey 2007and Guay 2008 For an introduction to relativistic quantum field theory, see, e.g., Brown & Harre 1988, Teller 1995, Cao 1999 …”

Conceptual Foundations of Yang–Mills Theories

“…To my knowledge such a proof exists only in the FQ. The implications of this proof for the status of the gauge principle, as a pragmatic principle, are discussed in (Guay, 2008).…”