ar X iv : g r - qc / 9 70 40 48 v 1 1 7 A pr 1 99 7 Should Metric Signature Matter in Clifford Algebra Formulations of Physical Theories ? ∗
نویسنده
چکیده
Standard formulation is unable to distinguish between the (+ + +−) and (−−−+) spacetime metric signatures. However, the Clifford algebras associated with each are inequivalent, R(4) in the first case (real 4 by 4 matrices), H(2) in the latter (quaternionic 2 by 2). Multivector reformulations of Dirac theory by various authors look quite inequivalent pending the algebra assumed. It is not clear if this is mere artifact, or if there is a right/wrong choice as to which one describes reality. However, recently it has been shown that one can map from one signature to the other using a tilt transformation[8]. The broader question is that if the universe is signature blind, then perhaps a complete theory should be manifestly tilt covariant. A generalized multivector wave equation is proposed which is fully signature invariant in form, because it includes all the components of the algebra in the wavefunction (instead of restricting it to half) as well as all the possibilities for interaction terms. Summary of talk at the Special Session on Octonions and Clifford Algebras, at the 1997 Spring Western Sectional Meeting of the American Mathematical Society, Oregon State University, Corvallis, OR, 19-20 April 1997. anonymous ftp://www.clifford.org/clf-alg/preprints/1995/pezz9502.latex Email: [email protected] or [email protected] Email: [email protected]
منابع مشابه
ar X iv : g r - qc / 9 70 40 54 v 1 1 9 A pr 1 99 7 The Nonlinear Quantum Gauge Theory – Superrelativity
A new type of nonlinear gauge quantum theory (superrelativity) has been proposed [1, 2, 3, 4, 5, 6]. Such theory demands a radical reconstruction of the quantum field conception and spacetime structure, and this paves presumably way to the comprehension of the quantum nature of inertia.
متن کاملar X iv : g r - qc / 9 50 40 38 v 1 2 4 A pr 1 99 5 CLOCK AND CATEGORY : IS QUANTUM GRAVITY ALGE
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing Topological Quantum Field theories. The algebraic structures are related to ideas about the reinterpretation of quantum mechanics in a general relativistic context.
متن کاملX iv : g r - qc / 9 30 40 14 v 1 1 2 A pr 1 99 3 The Fourth Root of Gravity ∗
By attaching basis vectors to the components of matter fields, one may render free action densities fully covariant. Both the connection and the tetrads are quadratic forms in these basis vectors. The metric of spacetime, which is quadratic in the tetrads, is then quartic in the basis vectors. ∗Submitted to the 1993 competition of the Gravity Research Foundation.
متن کاملar X iv : g r - qc / 9 70 80 05 v 1 4 A ug 1 99 7 Spacetime structure of an inflating global monopole
The evolution of a global monopole with an inflating core is investigated. An analytic expression for the exterior metric at large distances from the core is obtained. The overall spacetime structure is studied numerically, both in vacuum and in a radiation background.
متن کاملar X iv : g r - qc / 9 71 01 37 v 1 3 1 O ct 1 99 7 METRIC FLUCTUATIONS IN SEMICLASSICAL GRAVITY ∗
The Einstein-Langevin equation is a perturbative correction to the semiclassical Ein-stein equation which takes into account the lowest order quantum fluctuations of the matter stress-energy tensor. It predicts classical stochastic fluctuations in the metric field which may describe some of the remnant gravitational fluctuations after the process of environment induced decoherence driving the q...
متن کامل