Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.105006· OSTI ID:21502629

Shabad, Anatoly E ^[1]; Usov, Vladimir V ^[2]

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1. P.N. Lebedev Physics Institute, Moscow 117924 (Russian Federation)
2. Center for Astrophysics, Weizmann Institute, Rehovot 76100 (Israel)

In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum c=1, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we establish the positive convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants that are derivatives of the effective Lagrangian with respect to the field invariants. Violation of the general principles by the one-loop approximation in QED at exponentially large magnetic field is analyzed, resulting in complex energy ghosts that signal the instability of the magnetized vacuum. Superluminal excitations (tachyons) appear, too, but for the magnetic field exceeding its instability threshold. Also other popular Lagrangians are tested to establish that the ones leading to spontaneous vacuum magnetization possess wrong convexity.

• OSTI ID: 21502629
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.105006; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
CAUSALITY
DIELECTRIC MATERIALS
EXCITATION
INSTABILITY
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
MAGNETIZATION
NONLINEAR PROBLEMS
PERMITTIVITY
QUANTUM ELECTRODYNAMICS
TACHYONS
UNITARITY
VELOCITY
CALCULATION METHODS
DIELECTRIC PROPERTIES
ELECTRICAL PROPERTIES
ELECTRODYNAMICS
ELEMENTARY PARTICLES
ENERGY-LEVEL TRANSITIONS
FIELD THEORIES
FUNCTIONS
MATERIALS
PHYSICAL PROPERTIES
POSTULATED PARTICLES
QUANTUM FIELD THEORY