When a Poincaré-invariant system spontaneously breaks continuous internal symmetries, Goldstones’ theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincaré symmetry, however, the kinds of excitations that satisfy Goldstone’s theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone’s theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincaré symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations — including fermionic degrees of freedom — even when all symmetries are bosonic. To demonstrate its utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin s requires an \( \mathcal{N} \) = 2s supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a ‘spin-orbital’ coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.

当庞加莱不变系统自发地破坏连续的内部对称性时，戈德斯通定理要求存在与破坏的对称生成器一一对应的无质量自旋零激发。但是，当系统自发地打破庞加莱对称性时，满足戈德斯通定理的激发类型可能会很不正常。特别地，它们可以具有任何自旋，并且不必是粒子甚至准粒子。但是，用于制定Goldstones有效作用的标准陪伴结构相当局限，并且无法生成Goldstone定理所允许的全部可能性。我们通过为系统自发地打破庞加莱对称性的系统提出新颖的陪集结构，提出了对此问题的（部分）补救措施。即使所有对称性都是玻色的，这种新构造也能够通过各种戈德斯通激发（包括费米子自由度）产生有效的作用。为了证明其实用性，我们着重于为各种自旋的点粒子构造有效的动作。我们恢复了已知结果，即自旋粒子s要求\（\ mathcal {N} \） = 2 s超对称世界线重新参数化规范的对称性，我们在陪集构建的层次上实现该对称性。在这一过程中，我们发现无质量粒子需要一种新型的希格斯逆约束，这种约束与某些费米液体有效场理论中出现的动力学希格斯逆约束相似。然后，我们考虑除了量子自旋以外还具有有限空间范围并且可以自由旋转的粒子。我们推导了此类粒子的新颖作用，并发现了固有量子自旋与物理旋转自由度之间的“自旋轨道”耦合。