Semiclassical linear-stability analysis of homogeneous electric-field modes coupled to a scalar quantum field

Journal Article · Sat Sep 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2069· OSTI ID:6313374

Rogers, B ^[1]

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1. Center for Theoretical Physics, Laboratory for Nuclear Science Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA)

We examine the problem of a homogeneous, time-dependent electric field {ital E}({ital t}) in the presence of a scalar quantum field in its vacuum state, using the semiclassical Maxwell equations. We obtain the Laplace transform of {ital E}({ital t}) as a function of initial conditions in the linear approximation. For the case we study, this approximation is valid for a certain length of time which is increased indefinitely as the initial values of the electric field and other perturbation quantities are made vanishingly small. We find the existence of unphysical instabilities (exponentially growing modes) with an imaginary frequency which is shown to be identical to the homogeneous Landau ghost mode at the one-loop level in scalar QED. We show that this mode may be suppressed, however, by a certain restriction on the initial data, which then leads to asymptotically well-behaved solutions for {ital E}({ital t}). For {ital t}{much gt}{ital m}{sup {minus}1}, these solutions approach a constant value which differs from {ital E}(0) only by a small relative amount of {ital O}({alpha}) in general.

• DOE Contract Number: AC02-76ER03069
• OSTI ID: 6313374
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 42:6; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
VACUUM STATES
COUPLING
ELECTRIC FIELDS
LAPLACE TRANSFORMATION
MAXWELL EQUATIONS
PERTURBATION THEORY
PROPAGATOR
QUANTUM ELECTRODYNAMICS
RENORMALIZATION
SCALAR FIELDS
SEMICLASSICAL APPROXIMATION
STABILITY
TIME DEPENDENCE
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD THEORIES
INTEGRAL TRANSFORMATIONS
PARTIAL DIFFERENTIAL EQUATIONS
TRANSFORMATIONS
645400* - High Energy Physics- Field Theory