Novel Effects of Nonlinear Electrodynamics

1
Novel Effects of Nonlinear Electrodynamics

• Daniel Tennant
• CSU Fresno
• In collaboration with
• Gerardo Munoz

2
Properties of Maxwell EM

• Lorentz Covariance
• Lagrangian must be constructed out of Lorentz
  scalars
• Charge Conservation
• Gauge freedom in the four-potential
• Superposition
• Linear differential equations in E and B
• Causal Behavior
• No temporal derivatives higher than 2nd order
• Parity
• Exclude odd powers of the magnetic field

3
Generalizations to Maxwell

• What if we consider theories that do not abide by
  the principle of superposition?
• Implies that any power of the fields can should
  be found in the Lagrangian
• I consider only the first corrections to Maxwell

4
Effective Lagrangians

• Maxwell EM
• Generic Nonlinear EM

5
Equations of Motion

• Equations of motion in terms of Lorentz scalars
• Source-Free Euler-Lagrange Equations
• Become
• 
  
• with

6
Dielectric and Magnetic Permeability Tensors

• with

7
Plane wave through a Strong Background Field

• Starting with the spatial component of
• Two velocities are found for the two polarization
  modes
• where

8
QED

• The Euler-Heisenberg Lagrangian takes into
  account quantum corrections to Maxwells
  equations
• Values for coefficients of QED

9
Born-Infeld Lagrangian

• Proposed by the authors to deal with the problem
  of the electrons infinite self-energy
• They postulated a maximum value the electric
  field could attain, ß, by analogy with special
  relativity
• Expanding this lagrangian in small field strength

10
Birefringence

• Uniaxial dielectric mediums
  
• Ordinary and extraordinary waves are formed

11
Optical Rotation

• The polarization vector will rotate due to the
  different velocities of the two modes

12
Calculation of Rotations for QED

• Difference in phase
• Difference in polarization vector
  
• Note for Born-Infeld this effect is not possible

for initial polarization w.r.t. the
magnetic field
13
PVLAS CollaborationZavattini, Ruoso, Polacco,
arXiv0706.3419

• Our calculation
• PVLAS has ruled out rotations down to the level
  of
• rad at 5T.