Her work is a foundational document in quantum theory because it verifies the ancient insight that what is most important in any physical system is what remains the same in the system as the system is changing.ĭifferentiable symmetries belong to the much larger class of symmetrical transformations. In 1915, Emmy Noether demonstrated that differentiable symmetries give rise to conservation laws. It is a structure that appears when the symmetries of a quantum system are under analysis. Is there a deeper structure beneath the quantum formalism? Yes, of course there is. Matrices are particularly useful in quantum mechanics because, unlike the numbers, they do not necessarily commute under multiplication. Analytic functions, Fourier transforms, eigenvalues, and matrices all play their accustomed roles. The evolution of a system is specified by Schrödinger’s equation. Observables are represented as operators acting on quantum states. Wave functions are defined on a Hilbert space. 1 Quantum Theory, Groups and Representations is based on a series of lectures that he gave at Columbia University.Īn introduction to quantum mechanics very often follows a well-worn path. Educated at Harvard and at Princeton, Woit is known for his book Not Even Wrong, and for his blog of the same name. P eter Woit is a senior lecturer in the department of mathematics at Columbia University. Quantum Theory, Groups and Representations
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