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In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The…
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…
Quantum Electrodynamics can be formulated as the theory of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as an additional source for the electromagnetic field. The topological charge…
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the…
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving…
A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
There is a natural way to study the long distance interactions of gauge theories in the electric (momentum) representation. Here, the main ideas are presented for the Abelian and Yang-Mills gauge theories emphasizing on the structure and…
We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our…
The Standard Model of particle physics is built on the principle of local gauge symmetry. This work provides a pedagogical introduction for advanced undergraduates by using quantum electrodynamics (QED) as the simplest example of a gauge…
Infra-red divergences obscure the underlying soft dynamics in gauge theories. They remove the pole structures associated with particle propagation in the various Green's functions of gauge theories. Here we present a solution to this…
Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant…
We derive detailed and intergral fluctuation relations as well as a Thermodynamic Uncertainty Relation constraining the exchange statistics of an arbitrary number of non-commuting conserved quantities among two quantum systems in transport…
Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation.…
We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not…
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few…
In undergraduate electromagnetism courses, the Lorenz gauge condition is often presented as a convenient mathematical choice that decouples the wave equations for the scalar and vector potentials. While true, this presentation may leave…
The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In…