Fermions and bosons in a unified framework. II. Interacting models

Journal Article · Wed Nov 15 00:00:00 EST 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.18.3761· OSTI ID:6464584

Macrae, K I

We construct some fully interacting field theories. The first model has a colored, curved Weinberg-Salam-type action. It is formed by taking the Hilbert product of the (generalized) curvature of a (given) superalgebra with an auxiliary (generalized) curvature. Note that pieces of simple superalgebra are gauged, the effective superalgebra of gauge fields is not simple. The auxiliary curvature was needed to obtain the linear pieces of the action, and it thus appears to be somewhat cd hoc. In contrast we show how to construct an action using only the curvature of a local superalgebra without the auxiliary curvature (it is therefore quadratic). Nonetheless, linear terms arise as crossterms between pieces of the curvature. In fact, since we have chosen to use a special unitary flavor algebra and four-component spinors, we discover we have already specified a unique simple supergroup whose other Bose gauge fields are in U(2,2), the Lie algebra formed by all the Dirac matrices. These fields gauge the spin structure of the fermions. Color causes certain complications discussed in the paper. The tensor piece of the U(2,2) curvature consists of the usual curvasure plus a term identifiable at the old auxiliary tensor. Thus both linear and quadratic terms for the space-time curvature arise when the full curvature is squared. The field associated with the identity generator is electromagnetism; with the vector, torsion; with the tensor, curvature and auxiliary terms. We call the fields associated with the axial generators axial torsion and axial electromagnetism. When the fields which couple to Dirac spinors are assumed proportional to their scalar counterparts, an experimental value for a conserved axial electromagnetic coupling is 10/sup -3/e. We present a qualitative argument for the renormalizability of this action, since it is almost that of a standard Yang-Mills gauge theory, based on preservation of recoordinatization invariance by the quantization procedure.

• Research Organization: Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 6464584
• Journal Information: Phys. Rev., D; (United States), Vol. 18:10
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
BOSONS
FERMIONS
WEINBERG-SALAM GAUGE MODEL
SPINORS
COLOR MODEL
DIRAC EQUATION
ELECTROMAGNETIC INTERACTIONS
FERMI INTERACTIONS
HILBERT SPACE
RENORMALIZATION
SCALAR FIELDS
SPACE-TIME
VECTOR FIELDS
YANG-MILLS THEORY
BANACH SPACE
BASIC INTERACTIONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
INTERACTIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTICLE MODELS
QUARK MODEL
SPACE
UNIFIED GAUGE MODELS
WAVE EQUATIONS
WEAK INTERACTIONS
645400* - High Energy Physics- Field Theory