RELATIVISTIC INVARIANCE AND THE SQUARE-ROOT KLEIN-GORDON EQUATION

Journal Article · Tue Jan 01 04:00:00 EST 1963 · Journal of Mathematical Physics (New York) (U.S.)

DOI:https://doi.org/10.1063/1.1703882· OSTI ID:4761451

Sucher, J

Although the usual operator invariance requirements and corresponding commutation conditions encountered in the study of the invariance of relativistic wave equations (and other equations of physics) are sufficient conditions for invariance, they are by no means necessary. More general conditions are given and illustrated with the square-root Klein-Gordon equation. A new proof is thereby given of the Lorentz invariance of this equation. The methods developed are extended to cover the presence of external fields, and it is proved that the usual gauge invariant modification of the relativistic Hamiltonlan of a spinless particle which takes into account the presence of an external electromagnetic field leads, in the quantum mechanical case, to an equation which does not admit the proper Lorentz group. This theorem and its generalization are discussed in connection with Dirac's statement that the square-root equation cannot be extended to include interaction without losing Lorentz invariance. (auth)

• Research Organization: Univ. of Maryland, College Park
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-013363
• OSTI ID: 4761451
• Journal Information: Journal of Mathematical Physics (New York) (U.S.), Journal Name: Journal of Mathematical Physics (New York) (U.S.) Vol. Vol: 4; ISSN JMAPA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

COMMUTATION RELATIONS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
ELEMENTARY PARTICLES
FIELD THEORY
GAUGE INVARIANCE
GROUP THEORY
HAMILTONIAN
KLEIN-GORDON EQUATION
LORENTZ TRANSFORMATIONS
MOTION
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY
SPIN