Conformal symmetry and unification

AIP Conference Proceedings

2001

Abstract. Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since transformations to uniformly accelerated frames are naturally included in this conformally invariant description, the quantum algebra is also able to deal with uniformly accelerated motion.

Section: Conformal Dirac Electronmentioning

confidence: 99%

Quantum algebraic representation of localization and motion of a Dirac electron

AIP Conference Proceedings

2001

“…Poincaré and dilatation generators take the same form in terms of both sets of variables ( 9) and (17). The variables x µ and s µν are quantum operators as X µ and S µν but they obey canonical commutation relations…”

Section: Canonical Localization Variablesmentioning

confidence: 99%

“…Relations (15,17) thus show that canonical variables x µ and s µν are not hermitian. This is an important output of our quantum approach to the localization problem.…”

Section: Canonical Localization Variablesmentioning

confidence: 99%

See 1 more Smart Citation

Observable Dirac electron in accelerated frames

1999

Physics Letters A

We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame transformations are determined within a unique algebraic framework. Redshifts, i.e. shifts under transformations to uniformly accelerated frames, are evaluated and found to differ from the expressions of classical relativity.

“…Clearly the extension of these results to massive field theories is impossible as long as mass is treated as a classical constant which breaks conformal symmetry, as is the case in Dirac's electron theory [35]. In modern developments however, electron mass is generated through an interaction with Higgs fields [36] and standard forms of this interaction obey conformal invariance [37]. Mass is no longer a classical constant.…”

Section: Introductionmentioning

confidence: 99%

Quantum hexaspherical observables for electrons

2000

Annalen der Physik

A new quantum algebraic description of relativistic electrons, built on a conformal dynamical symmetry (SO(4,2 )), has recently been proposed to treat localization in space‐time. It is shown here that localization of an electron may be represented by components of a SO(4,2) vector which are quantum generalizations of the hexaspherical coordinates of classical projective geometry. The shift of this vector under transformations to uniformly accelerated frames is described by SO(4,2) rotations. Hexaspherical observables also allow one to represent the quantum law of free fall under a form explicitly compatible with the same dynamical symmetry.