Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay

Abstract

This paper explores the properties of the Pauli-Lubanski spin vector for the general motion of spin-1/2 particles in curved space-time. Building upon previously determined results in flat space-time, it is shown that the associated Casimir scalar for spin possesses both gravitational contributions and frame-dependent contributions due to non-inertial motion, where the latter represents a possible quantum violation of Lorentz invariance that becomes significant at the Compton wavelength scale. When applied to muon decay near the event horizon of a microscopic Kerr black hole, it is shown that its differential cross section is strongly affected by curvature, with particular sensitivity to changes in the black hole's spin angular momentum. In the absence of curvature, the non-inertial contributions to the decay spectrum are also identified and explored in detail, where its potential for observation is highest for large electron opening angles. It is further shown how possible contributions to noncommutative geometry can emerge from within this formalism at some undetermined length scale. Surprisingly, while the potential exists to identify noncommutative effects in muon decay, the relevant terms make no contribution to the decay spectrum, for reasons which remain unknown.

19 pages, 15 figures; REVTeX file; v5. corrections to references; Accepted for publication in Phys. Rev. D

References in corpus (22)

• Black Holes at the LHC
• Gravity coupled with matter and foundation of non-commutative geometry
• Loop Quantum Gravity
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Quantum Gravity: a Progress Report
• The motion of point particles in curved spacetime
• A Classical Sequential Growth Dynamics for Causal Sets
• Noncommutative Geometry and Gravity
• Noncommutative Quantum Gravity
• Gravitational Couplings of Intrinsic Spin
• Measurement Theory and General Relativity
• Do black holes radiate?
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Tidal Dynamics in Cosmological Spacetimes
• Indications of causal set cosmology
• Helicity Precession of Spin-1/2 Particles in Weak Inertial and Gravitational Fields
• Tidal Dynamics in Kerr Spacetime
• Riemannian Geometry of Noncommutative Surfaces
• First Order Radiative Corrections to Polarized Muon Decay Spectrum
• Gravitationally induced electromagnetism at the Compton scale
• The implications of noninertial motion on covariant quantum spin
• Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time

Cited by in corpus (7)

• Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung
• Fermionic one-particle states in curved spacetimes
• Breakdown of Casimir Invariance in Curved Space-Time
• General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles
• Local Space-Time Curvature Effects on Quantum Orbital Angular Momentum
• Solution to the $\beta$-functions in Lorentz-violating theories as a decomposition into irreducible representations
• Is There an Observable Limit to Lorentz Invariance at the Compton Wavelength Scale?