Abstract
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.
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References
L. Alberte and A. Nicolis, Spontaneously broken boosts and the Goldstone continuum, JHEP 07 (2020) 076 [arXiv:2001.06024] [INSPIRE].
Steven Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press, (1996).
D. V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3 [INSPIRE].
V. I. Ogievetsky, Nonlinear realizations of internal and space-time symmetries, in X-th winter school of theoretical physics in Karpacz, Poland (1974).
E. Ivanov and V. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 1050.
L. V. Delacrétaz, S. Endlich, A. Monin, R. Penco and F. Riva, (Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects, JHEP 11 (2014) 008 [arXiv:1405.7384] [INSPIRE].
H. Watanabe and T. Brauner, On the number of Nambu-Goldstone bosons and its relation to charge densities, Phys. Rev. D 84 (2011) 125013 [arXiv:1109.6327] [INSPIRE].
T. Brauner and H. Watanabe, Spontaneous breaking of spacetime symmetries and the inverse Higgs effect, Phys. Rev. D 89 (2014) 085004 [arXiv:1401.5596] [INSPIRE].
M. J. Landry, The coset construction for non-equilibrium systems, JHEP 07 (2020) 200 [arXiv:1912.12301] [INSPIRE].
M. J. Landry, Second sound and non-equilibrium effective field theory, arXiv:2008.11725 [INSPIRE].
I. Z. Rothstein and P. Shrivastava, Symmetry Realization via a Dynamical Inverse Higgs Mechanism, JHEP 05 (2018) 014 [arXiv:1712.07795] [INSPIRE].
I. Z. Rothstein and P. Shrivastava, Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit, Phys. Rev. B 99 (2019) 035101 [arXiv:1712.07797] [INSPIRE].
J. W. van Holten, D = 1 supergravity and spinning particles, hep-th/9510021 [INSPIRE].
M. Baggioli and M. Landry, Effective Field Theory for Quasicrystals and Phasons Dynamics, SciPost Phys. 9 (2020) 062 [arXiv:2008.05339] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
I. Low and A. V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. A. Rosen, More on gapped Goldstones at finite density: More gapped Goldstones, JHEP 11 (2013) 055 [arXiv:1306.1240] [INSPIRE].
S. Endlich, A. Nicolis and R. Penco, Ultraviolet completion without symmetry restoration, Phys. Rev. D 89 (2014) 065006 [arXiv:1311.6491] [INSPIRE].
A. Nicolis, R. Penco and R. A. Rosen, Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].
G. Goon, A. Joyce and M. Trodden, Spontaneously Broken Gauge Theories and the Coset Construction, Phys. Rev. D 90 (2014) 025022 [arXiv:1405.5532] [INSPIRE].
S. J. Gates, M. T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
J. W. van Holten, Propagators and path integrals, Nucl. Phys. B 457 (1995) 375 [hep-th/9508136] [INSPIRE].
A. Frydryszak, Lagrangian models of the particles with spin: The First seventy years, hep-th/9601020 [INSPIRE].
H. Ikemori, Superfield formulation of superparticles, Z. Phys. C 44 (1989) 625 [INSPIRE].
P. S. Howe, S. Penati, M. Pernici and P. K. Townsend, Wave Equations for Arbitrary Spin From Quantization of the Extended Supersymmetric Spinning Particle, Phys. Lett. B 215 (1988) 555 [INSPIRE].
J. P. Edwards and C. Schubert, Quantum mechanical path integrals in the first quantised approach to quantum field theory, arXiv:1912.10004 [INSPIRE].
R. Marnelius, Proper BRST quantization of relativistic particles, Nucl. Phys. B 418 (1994) 353 [hep-th/9309002] [INSPIRE].
M. J. Landry, Dynamical chemistry: non-equilibrium effective actions for reactive fluids, arXiv:2006.13220 [INSPIRE].
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Landry, M.J., Sun, G. The coset construction for particles of arbitrary spin. J. High Energ. Phys. 2021, 40 (2021). https://doi.org/10.1007/JHEP05(2021)040
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DOI: https://doi.org/10.1007/JHEP05(2021)040