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Novel duality-invariant theories of electrodynamics

Ángel J. Murcia

Abstract

We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a single seed duality-invariant theory. If the seed theory is causal, the theories constructed from this method will also be causal when the parameter is non-negative. On the other hand, we find two additional novel families of duality-invariant theories which include a nonzero term independent of the electromagnetic field. The first of them generalizes Bialynicki-Birula electrodynamics, while the second family of theories features a well-defined Maxwell limit as the term independent of the gauge field strength is sent to zero.

Novel duality-invariant theories of electrodynamics

Abstract

We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a single seed duality-invariant theory. If the seed theory is causal, the theories constructed from this method will also be causal when the parameter is non-negative. On the other hand, we find two additional novel families of duality-invariant theories which include a nonzero term independent of the electromagnetic field. The first of them generalizes Bialynicki-Birula electrodynamics, while the second family of theories features a well-defined Maxwell limit as the term independent of the gauge field strength is sent to zero.

Paper Structure

This paper contains 3 sections, 2 theorems, 54 equations.

Table of Contents

  1. Duality-invariance condition with $\psi \neq 0$ in the Hamiltonian formalism
  2. Instances of dynamical choices for $\psi$
  3. Solving \ref{['eq:spdual']} and \ref{['eq:hdifcond']} perturbatively

Key Result

Theorem 1

Let $\mathcal{L}_0(s,p)$ be a given duality-invariant theory. Then the one-parameter family of theories $\mathcal{M}_\gamma(\mathcal{L}_0)(s,p)=\mathcal{L}_0(\mathcal{L}_\gamma^{\mathrm{MM}}(s,p),p)$ is duality-invariant.

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Theorem 2
  • proof
  • Example 5
  • Example 6