Symmetry Breaking

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Focusing on spontaneous symmetry breaking, this text offers a rigorous exploration of its mathematical foundations in classical field theory, aimed at graduate students. It highlights the importance of non-symmetric ground states and the infinite extension of systems. Key topics include the existence of disjoint Hilbert space sectors, which parallel phases in statistical mechanics and representations in quantum field theory. The discussion emphasizes locality and stability, providing insights into the physical implications of these mathematical concepts and their connection to stability criteria in infinite-dimensional systems.