We examine symmetry breaking in field theory within the framework of derived geometry, as applied to field theory via the Batalin–Vilkovisky formalism. Our emphasis is on the standard examples of Ginzburg–Landau and Yang–Mills–Higgs theories and is primarily interpretive. The rich, sophisticated language of derived geometry captures the physical story elegantly, allowing for sharp formulations of slogans (e.g., for the Higgs mechanism, that the unstable ghosts feed the Goldstone bosons to a hungry, massless gauge boson). Rewriting these results in the BV formalism provides, as one nice payoff, a reformulation of ’t Hooft’s family of gauge-fixing conditions for spontaneously broken gauge theory that behaves well in the $\xi \to \infty$ limit.

我们通过派塔林-维尔科维斯基形式主义将场论应用于对称场理论中，研究了场论在对称理论中的突破。我们的重点是金茨堡-兰道和杨-米尔斯-希格斯理论的标准例子，并且主要是解释性的。派生几何的丰富，精巧的语言优雅地捕捉了真实的故事，从而形成了清晰的口号（例如，对于希格斯机制，不稳定的鬼魂将戈德斯通玻色子喂入了饥饿的，无质量的玻色子）。用BV形式主义重写这些结果，作为一个不错的回报，是对自发破碎的规范理论中't Hooft的规范固定条件族的重新表述，该理论在规范中表现良好。$\xi \to \infty$ 限制。