Self-dual Maxwell field on a null surface. II

• Published in: Foundations of physics 1994-04, Vol.24 (4), p.467-476
• Main Author: GOLDBERG, J. N
• Format: Article
• Language: English
• Subjects: CANONICAL TRANSFORMATIONS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Classical and quantum physics: mechanics and fields; Classical electromagnetism, maxwell equations; Classical field theories; DIFFERENTIAL EQUATIONS; EQUATIONS; Exact sciences and technology; FIELD THEORIES; Field theory; GAUGE INVARIANCE; GENERAL RELATIVITY THEORY; General theory of fields and particles; HAMILTON-JACOBI EQUATIONS; INVARIANCE PRINCIPLES; Lagrangian and hamiltonian approach; PARTIAL DIFFERENTIAL EQUATIONS; Physics; QUANTIZATION; Quantum electrodynamics; QUANTUM FIELD THEORY; QUANTUM GRAVITY; Specific calculations; Specific theories and interaction models; particle systematics; The physics of elementary particles and fields; TRANSFORMATIONS 661310 > Relativity & Gravitation-- (1992-)
• ISSN: 0015-9018; 1572-9516
• DOI: 10.1007/BF02058058

The canonical formalism for the Maxwell field on a null surface has been revisited. A new pair of gauge-independent canonical variables is introduced. It is shown that these variables are derivable from a Hamilton-Jacobi functional. The construction of the appropriate C algebra is carried out in preparation for quantization. The resulting quantum theory is similar to a previous result. It is then shown that one can construct the T-variables of Rovelli and Smolin on the null surface. The Poisson bracket algebra exhibits causal relations along the null rays, but is nonsingular if the loops are restricted to those whose projections along the null rays are not tangent and one-to-one. Finally, there is a brief discussion of the relevance of this work to general relativity. 18 refs.