Spontaneously broken spacetime symmetries and Goldstone's theorem

Area of Science:

• Theoretical Physics
• High Energy Physics
• Condensed Matter Theory

Background:

• Goldstone's theorem links broken symmetry generators to massless modes.
• The standard theorem fails for spontaneously broken spacetime symmetries.
• Existing methods do not consistently yield the correct count of massless modes.

Purpose of the Study:

• To provide a general method for correctly counting massless modes.
• To resolve the failure of naive generalizations of Goldstone's theorem.
• To analyze massless modes in spontaneously broken Poincaré and conformal symmetries.

Main Methods:

• Revisiting the theoretical framework of spontaneous symmetry breaking.
• Developing a generalized counting procedure for massless modes.
• Applying the method to specific examples of spacetime symmetries.

Main Results:

• A corrected method for enumerating massless modes in spontaneously broken theories.
• Demonstration of the method's efficacy for Poincaré and conformal symmetries.
• Resolution of the long-standing issue with naive mode counting.

Conclusions:

• The generalized method accurately predicts massless modes for broken spacetime symmetries.
• This work clarifies the application of Goldstone's theorem in complex symmetry breaking scenarios.
• The findings have implications for understanding particle physics and condensed matter systems.