Combined Lorentz Symmetry: Lessons from Superfluid He

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Condensed Matter Physics

Background:

• The fundamental symmetries of the relativistic quantum vacuum, including P, T, and Lorentz symmetry, are examined.
• Symmetry breaking in condensed matter systems, specifically superfluid phases of liquid Helium-3, provides a framework for understanding vacuum symmetries.
• Gravitational tetrads are proposed as order parameters for symmetry breaking in the quantum vacuum.

Purpose of the Study:

• To investigate the combined P, T, and Lorentz symmetry of the relativistic quantum vacuum.
• To explore symmetry breaking mechanisms in condensed matter systems and their implications for fundamental physics.
• To apply these concepts to address the cosmological constant problem.

Main Methods:

• Analysis of symmetry breaking in condensed matter vacua, specifically the Helium-3 A and B phases.
• Utilizing gravitational tetrads as order parameters to describe symmetry breaking.
• Investigating the topological consequences of vacuum degeneracy, such as torsion strings.

Main Results:

• Two scenarios for the origin of combined Lorentz symmetry are realized in superfluid Helium-3.
• Symmetry breaking in the Minkowski vacuum leads to continuous degeneracy and topological defects like torsion strings.
• Fourfold degeneracy related to P and T symmetries suggests distinct tetrad fields for Weyl fermions and antiparticles, potentially breaking the equivalence principle.

Conclusions:

• The study proposes a novel framework for understanding quantum vacuum symmetries through condensed matter analogs.
• The findings suggest implications for theories of gravity with multiple metric fields and parity violation.
• The application of gravitational tetrads offers a potential pathway towards resolving the cosmological constant problem.