LOCAL CONFORMAL INVARIANCE OF THE WAVE EQUATION FOR FINITE COMPONENT FIELDS. I. THE CONDITIONS FOR INVARIANCE, AND FULLY REDUCIBLE FIELDS
198222 pages
Published in:
- J.Math.Phys. 23 (1982) 1925-1946
DOI:
View in:
Citations per year
Abstract: (AIP)
The conditions for local conformal‐invariance of the wave equation are obtained for finite‐component fields, of Types Ia and Ib [in the terminology of Mack and Salam, Ann. Phys. 5 3, 174 (1969).] These conditions generate a set of locally invariant free massless field equations and restrict the relevant representation of the Lie algebra [(k 4⊕d)⊕sl(2,C)] in the index space of the field to belong to a certain class. Those fully‐reducible representations which are in this class are described in full. The corresponding Type Ia field equations include only the massless scalar fieldequation,neutrinoequations,Maxwell’sequations, and the Bargmann–Wigner equations for massless fields of arbitrary helicity, and no others. In particular, it is confirmed [Bracken, Lett. Nuovo Cimento 2, 574 (1971)] that not all Poincaré‐invariant sets of massless Type Ia field equations are conformal‐invariant, contrary to some often‐quoted results of McLennan [Nuovo Cimento 3, 1360 (1956)], which are shown to be invalid. It is also shown that in the case of a potential, the wave equation is never conformal‐invariant in the strong sense (excluding gauge transformations).- INVARIANCE: CONFORMAL
- group: SL(2,C)
- GROUP THEORY: REPRESENTATION
- FIELD THEORY: MASSLESS
- MASSLESS: FIELD THEORY
- FIELD EQUATIONS: SOLUTION
- SPIN: 1/2
- 1/2: SPIN
- NEUTRINO: FIELD THEORY
- Dirac equation
References(0)
Figures(0)
0 References