# From Philosophical Reflections on Gauge Symmetries to Gauge-Invariant Approaches to (Particle) Physics

Graz

Austria

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Modern physics is written in the language of *gauge* field theories. The Standard Model of particle physics is a gauge theory in the sense that it rests on internal *local* symmetries. General relativity is a gauge theory in the sense that it rests on an external *local* symmetry. Given the pivotal role of gauge (i.e. local) symmetries in modern physics, it is imperative to thoroughly study their conceptual underpinnings. One central topic of this workshop concerns the*ontological* status of gauge symmetries. Should they be interpreted as mere mathematical structure of our *descriptions* of reality or do they *represent the structure* of reality? There is some noticeable consensus among physicists and philosophers that (i) gauge symmetries are not physically real but rather are mathematical redundancy and that (ii) physically real quantities must be gauge-invariant.

However, as has been pointed out by several researchers, if this is so, then we find worrisome conflicting assumptions at the very heart of modern particle physics. For instance, textbook approaches to the BEH mechanism imply that the Higgs field gives mass to particles via the spontaneous symmetry breaking of a gauge symmetry. But how could the breaking of unphysical mathematical redundancy have any physical impact on our world? Furthermore, given the fact that each and every “elementary” field/particle in the Standard Model Lagrangian is actually a gauge-variant quantity, their link with the actual fields/particles experimentally detected is a non-trivial and standing issue. When we turn from quantum field theory to the other pillar of modern physics, general relativity, the first thing to note is that GR is invariant under arbitrary differentiable coordinate transformations, which means that the theory is based on an external local symmetry referred to as general covariance or diffeomorphism invariance. This invariance under diffeomorphisms of the manifold is often assumed to imply that the manifold and its point cannot be considered physical quantities. In this sense, time coordinates and time evolution become gauge-dependent in GR which leads to several questions regarding the nature of time.

Where does this leave us? The thesis to be discussed in the course of this workshop is whether such tensions and conceptual problems can be resolved by pursuing gauge-invariant approaches. Examples of facilitation of gauge-invariant approaches are lattice formulations, the Fröhlich-Morchio-Strocchi mechanism, and the dressing field method as they have been discussed e.g. in __arXiv:2110.00616.__

The aim of this workshop is to bring together philosophers and physicists in order to discuss the nature of gauge symmetries, reflect on the significance of the gauge principle, clarify virtues of and obstacles to gauge-invariant approaches, and shed light on ontological implications of such approaches.

Topics and questions we want to discuss include but are not limited to:

**1. The nature of gauge symmetries**

Are gauge symmetries physical symmetries, symmetries of nature, or are they mere descriptive redundancy? Do they have direct empirical significance? Or do we perhaps need a more refined classification according to which certain gauge symmetries exhibit specific physical signatures, while others do not? What does it mean to say that a gauge symmetry is spontaneously broken? Can only gauge-invariant quantities be physically real?

**2. Gauge-invariant approaches**

What can be achieved by pursuing gauge-invariant approaches? What are the virtues of and obstacles to gauge-invariant approaches? What are the ontological implications of approaches like the FMS? What are the ontological implications of the dressing field method? Can we expect that experimental results will confirm/suggest such approaches? What distinguishes the dressing field method from gauge fixing?

**3. Physical space-time**

Stripping general relativity off its symmetries, i.e., eliminating diffeomorphism and local Lorentz symmetries, may hint at the nature of the fundamental d.o.f. from which spacetime d.o.f. emerge. Some quantum gravity seems to suggest as much, notably LQG, causal dynamical triangulation, and causal sets. So may methods allowing formulations entirely in terms of gauge-invariant quantities, such as the FMS mechanism and the dressing field approach. Then, new challenges arise: For instance, cosmology is typically approached from within a fixed metric and cosmological time defined via a special choice of gauge. Accordingly, it is non-trivial to specify a manifestly gauge-invariant cosmological dynamics.

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