"First, without a physical interpretation, a purely mathematical structure, here a Lie algebra, would have no empirical content. Second, if we interpret the Lie algebra in terms of physical structures, taking electromagnetic and weak currents as its representations, then we have physical content, but only at the phenomenological level. In order to understand the physical structures (the currents) properly, we have to move deeper onto the level of their constituents (hadrons or quarks) and their dynamics so that we can have a dynamic understanding of the behavior of the currents, and thus of many features of current algebra and of reasons why current algebra is so successful." (Tian Yu Cao,"From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism", 2010)
"The underlying idea of current algebra, light-cone current algebra included, was to exploit the broken symmetry of strong interactions. The idea was pursued through abstracting physical predictions, as the consequences of the symmetry and in the form of certain algebraic relations obeyed by weak and electromagnetic currents of hadrons to all orders in strong interactions, from some underlying mathematical field theoretical models of hadrons and their interactions, more specifically from models of quark fields universally coupled to a neutral gluon field." (Tian Yu Cao,"From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism", 2010)
"Rotations and translations are global symmetries: they apply uniformly across the whole of space and time. A rotation about some axis rotates every point in space through the same angle. Gauge symmetries are different: they are local symmetries, which can vary from point to point in space. In the case of electromagnetism, these local symmetries are changes of phase. A local oscillation of the electromagnetic field has both an amplitude (how big it is) and a phase (the time at which it reaches its peak)." (Ian Stewart, "Symmetry: A Very Short Introduction", 2013)
"The classical theories of space, time, and matter were brought to their peak in James Clerk Maxwell’s equations for electromagnetism. This elegant system of equations unified two of nature’s forces, previously thought to be distinct. In place of electricity and magnetism, there was a single electromagnetic field. A field pervades the whole of space, as if the universe were filled with some kind of invisible fluid. At each point of space we can measure the strength and direction of the field, as if that fluid were flowing in mathematical patterns. For some purposes the electromagnetic field can be split into two components, the electric field and the magnetic field. But a moving magnetic field creates an electric one, and conversely, so when it comes to dynamics, both fields must be combined into a single more complex one." (Ian Stewart, "Visions of Infinity", 2013)
"The invariance of physical laws with respect to position or orientation (i.e., the symmetry of space) gives rise to conservation laws for linear and angular momentum. Sometimes the implications of symmetry invariance are far more complicated or sophisticated than might at first be supposed; the invariance of the forces predicted by electromagnetic theory when measurements are made in observation frames moving uniformly at different speeds (inertial frames) was an important clue leading Einstein to the discovery of special relativity. With the advent of quantum mechanics, considerations of angular momentum and spin introduced new symmetry concepts into physics. These ideas have since catalyzed the modern development of particle theory." (George B Arfken et al, "Mathematical Methods for Physicists: A comprehensive guide", 2013)
"Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability - which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948." (Steven Weinberg, CERN Courier, [interview with Matthew Chalmers] 2017)
"Euler’s formula - although deceptively simple - is actually staggeringly conceptually difficult to apprehend in its full glory, which is why so many mathematicians and scientists have failed to see its extraordinary scope, range, and ontology, so powerful and extensive as to render it the master equation of existence, from which the whole of mathematics and science can be derived, including general relativity, quantum mechanics, thermodynamics, electromagnetism and the strong and weak nuclear forces! It’s not called the God Equation for nothing. It is much more mysterious than any theistic God ever proposed." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)
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