Quantization of Gel'fand--Yaglom equations for free fields of arbitrary spin

Journal Article · Tue Jan 01 04:00:00 EST 1974 · J. Phys., A (London), v. 7, no. 1, pp. 1-11

DOI:https://doi.org/10.1088/0305-4470/7/1/007· OSTI ID:4336784

Cox, W

The Gel'fand-Yaglom equations for free fields of arbitrary spin, in the particular case when the field transforms according to a direct sum of inequivalent, irreducible finite representations of the proper Lorentz group are considered. Under the assumption that the theory carries neither physical states of zero charge or energy density and that the mass --spin states are nondegenerate, the precise forms of the minimal and characteristic polynomials of the s blocks of the L/sub 0/-matrix are obtained, and are then used to obtain new necessary and sufficient conditions that the theory be quantizable. The representation, according to which the field transforms, can be depicted graphically in a simple way and advantage is taken of this to use some simple ideas of graph theory to obtain the present results. This graphical approach is useful in practical and theoretical considerations in the theory. One conclusion is that it will probably be necessary to allow repeated irreducible representations of the proper Lorentz group for theories of spin greater than eight to be quantizable. (auth)

• Research Organization: Aston Univ., Birmingham, Eng.
• NSA Number: NSA-29-023362
• OSTI ID: 4336784
• Journal Information: J. Phys., A (London), v. 7, no. 1, pp. 1-11, Journal Name: J. Phys., A (London), v. 7, no. 1, pp. 1-11; ISSN JPAGB
• Country of Publication: United Kingdom
• Language: English

Related Subjects

*QUANTUM FIELD THEORY-- SPIN
DIAGRAMS
FIELD EQUATIONS
IRREDUCIBLE REPRESENTATIONS
LORENTZ GROUPS
MASS
MATRICES
N76200* --Physics (Theoretical)--Quantum Field Theories