First-order classical Lagrangians for the nonminimal Standard-Model Extension

Abstract

In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal Standard-Model Extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. First of all, a suitable Ansatz is made for the Lagrangian of the spin-degenerate operators $\hat{a}$, $\hat{c}$, $\hat{e}$, and $\hat{f}$ at leading order in Lorentz violation. The latter is shown to satisfy the set of five nonlinear equations that govern the map from the field theory to the classical description. After doing so, the second step is to propose results for the spin-nondegenerate operators $\hat{b}$, $\hat{d}$, $\hat{H}$, and $\hat{g}$. Although these are more involved than the Lagrangians for the spin-degenerate ones, an analytical proof of their validity is viable, nevertheless. The final step is to combine both findings to produce a generic Lagrangian for the complete set of Lorentz-violating operators that is consistent with the known minimal and nonminimal Lagrangians found in the literature so far. The outcome reveals the leading-order structure of the classical SME analog. It can be of use for both phenomenological studies of classical bodies in gravitational fields and conceptual work on explicit Lorentz violation in gravity. Furthermore, there may be a possible connection to Finsler geometry.

arXiv comment23 pages

References in corpus (34)

• Quantum Gravity at a Lifshitz Point
• Lorentz-Violating Extension of the Standard Model
• CPT Violation and the Standard Model
• Data Tables for Lorentz and CPT Violation
• Gravity, Lorentz Violation, and the Standard Model
• Noncommutative Field Theory and Lorentz Violation
• Nonstandard optics from quantum spacetime
• CPT, Strings, and Meson Factories
• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• CPT Violation Implies Violation of Lorentz Invariance
• Neutrinos with Lorentz-violating operators of arbitrary dimension
• Fermions with Lorentz-violating operators of arbitrary dimension
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Classical kinematics for Lorentz violation
• Waves on Noncommutative Spacetime and Gamma-Ray Bursts
• Spacetime foam, CPT anomaly, and photon propagation
• A CPT anomaly
• On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance
• Bounds on length scales of classical spacetime foam models
• Classical-physics applications for Finsler $b$ space
• Eliminating the CPT-Odd f Coefficient from the Lorentz-Violating Standard Model Extension
• Finsler-like structures from Lorentz-breaking classical particles
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Classical Lagrangians for Momentum Dependent Lorentz Violation
• Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields
• Z-string global gauge anomaly and Lorentz non-invariance
• CPT anomaly: a rigorous result in four dimensions
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Theory and Phenomenology of Spacetime Defects
• Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action
• From classical Lagrangians to Hamilton operators in the Standard-Model Extension

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• Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields
• Lorentz violation in Dirac and Weyl semimetals
• Lorentz and CPT Tests with Clock-Comparison Experiments
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Searches for beyond-Riemann gravity
• Searching for CPT Violation with Neutral-Meson Oscillations
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• Implications of $\text{SU}(2{)}_L$ gauge invariance for constraints on Lorentz violation
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
• Meson scattering in a Lorentz-violating scalar QED at finite temperature
• Characteristic tensors for almost Finsler manifolds