From classical Lagrangians to Hamilton operators in the Standard-Model Extension

Abstract

In this article we investigate whether a theory based on a classical Lagrangian for the minimal Standard-Model Extension (SME) can be quantized such that the result is equal to the corresponding low-energy Hamilton operator obtained from the field-theory description. This analysis is carried out for the whole collection of minimal Lagrangians found in the literature. The upshot is that first quantization can be performed consistently. The unexpected observation is made that at first order in Lorentz violation and at second order in the velocity the Lagrangians are related to the Hamilton functions by a simple transformation. Under mild assumptions, it is shown that this holds universally. This result is used successfully to obtain classical Lagrangians for two complicated sectors of the minimal SME that have not been considered in the literature so far. Therefore, it will not be an obstacle anymore to derive such Lagrangians even for involved sets of coefficients - at least to the level of approximation stated above.

35 pages, 1 figure

References in corpus (22)

• Quantum Gravity at a Lifshitz Point
• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• Classical kinematics for Lorentz violation
• Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
• Bounds on length scales of classical spacetime foam models
• One-Loop Renormalization of Pure Yang-Mills with Lorentz Violation
• Classical-physics applications for Finsler $b$ space
• One-Loop Renormalization of the Electroweak Sector with Lorentz Violation
• Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension
• One-Loop Renormalization of QCD with Lorentz Violation
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Quantization and stability of bumblebee electrodynamics
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Velocity in Lorentz-Violating Fermion Theories
• Generation of higher derivatives operators and electromagnetic wave propagation in a Lorentz-violation scenario
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Renormalizability of Yang-Mills theory with Lorentz violation and gluon mass generation
• Gupta--Bleuler's quantization of the anisotropic parity-even and CPT-even electrodynamics of standard model extension

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• Lorentz and CPT Tests with Clock-Comparison Experiments
• Testing local Lorentz invariance with short-range gravity
• Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators
• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Lorentz and CPT tests with charge-to-mass ratio comparisons in Penning traps
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• First-order classical Lagrangians for the nonminimal Standard-Model Extension
• Fermionic Lorentz violation and its implications for interferometric gravitational-wave detection
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
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