### Abstract

The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space-time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space-time. This invariance then dictates that the Clifford algebra generators be functions of space-time and is implemented by introducing new fields, the drehbeins ("spin legs"), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the "kinetic" Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space-time.

Original language | English (US) |
---|---|

Pages (from-to) | 2701-2718 |

Number of pages | 18 |

Journal | Journal of Mathematical Physics |

Volume | 35 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1994 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*35*(6), 2701-2718. https://doi.org/10.1063/1.530532

}

*Journal of Mathematical Physics*, vol. 35, no. 6, pp. 2701-2718. https://doi.org/10.1063/1.530532

**Local automorphism invariance : Gauge boson mass without a Higgs particle.** / Crawford, James P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Local automorphism invariance

T2 - Gauge boson mass without a Higgs particle

AU - Crawford, James P.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space-time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space-time. This invariance then dictates that the Clifford algebra generators be functions of space-time and is implemented by introducing new fields, the drehbeins ("spin legs"), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the "kinetic" Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space-time.

AB - The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space-time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space-time. This invariance then dictates that the Clifford algebra generators be functions of space-time and is implemented by introducing new fields, the drehbeins ("spin legs"), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the "kinetic" Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space-time.

UR - http://www.scopus.com/inward/record.url?scp=21344498700&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344498700&partnerID=8YFLogxK

U2 - 10.1063/1.530532

DO - 10.1063/1.530532

M3 - Article

AN - SCOPUS:21344498700

VL - 35

SP - 2701

EP - 2718

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -