The Principles of Gauging

Abstract

The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local symmetries of the free matter-field Lagrangian, in the following referred to as "conservation principle" and "gauge principle". Since both these express nothing but certain symmetry features of the free field theory, they are not sufficient to derive a true interaction coupling to a new gauge field. For this purpose it is necessary to advocate a third, truly empirical principle which may be understood as a generalization of the equivalence principle. The second task of the paper is to deal with the ontological question concerning the reality status of gauge potentials in the light of the proposed logical structure of gauge theories. A nonlocal interpretation of topological effects in gauge theories and, thus, the non-reality of gauge potentials in accordance with the generalized equivalence principle will be favoured.

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 …”

Holism and structuralism in U(1) gauge theory

“…12 Similar critical readings of the gauge principle have been discussed in the last years by the following authors: Brown (1999), Healey (2001), Lyre (2000Lyre ( , 2001, Martin (2002Martin ( , 2003, and Teller (2000).-One may however, as indeed Paul Teller in an unpublished draft (1999) contrary to his 2000 publication does, raise the objection that the above analysis of the application of the gauge argument in ordinary quantum wave mechanics fails, since-as differential operators-position and momentum are strictly speaking no linear operators on the Hilbert space L 2 (R), i.e. they cannot be defined on all vectors of L 2 (R) but only on a dense subset of differentiable functions thereof.…”

Geometric foundations of classical Yang–Mills theory

“…If we did not consider them physically equivalent, the resulting theory would be indeterministic. 21 In other words, this "radical form of indeterminism" (Earman & Norton, 1987, p. 515) would be the price to pay for what we could call internal substantivalism. By interpreting the different solutions as different representations of a single physical configuration, it is possible to recover a deterministic theory.…”

“…The most singular features of BRST symmetry, namely its action over an extended phase space and its global nature, follow naturally from this characterization. 21 It is a well known fact that in gauge theories the specification of a set of initial conditions for all the degrees of freedom determine infinitely many subsequent evolutions (Henneaux & Teitelboim, 1994).…”