Speaker:  Shinji Mukohyama (Kavli IPMU)

Date: 14:00, Monday March 4

Title: From configuration to dynamics -- Emergence of Lorentz signature
in classical field theory

Abstract: The Lorentzian metric structure used in any field theory
allows one to implement the relativistic notion of causality and to
define a notion of time dimension. This article investigates the
possibility that at the microscopic level the metric is Riemannian, i.e.
locally Euclidean, and that the Lorentzian structure, that we usually
consider as fundamental, is in fact an effective property that emerges
in some regions of a 4-dimensional space with a positive definite
metric. In such a model, there is no dynamics nor signature flip across
some hypersurface; instead, all the fields develop a Lorentzian dynamics
in these regions because they propagate in an effective metric. It is
shown that one can construct a decent classical field theory for
scalars, vectors and (Dirac) spinors in flat spacetime. It is then shown
that gravity can be included but that the theory for the effective
Lorentzian metric is not general relativity but of the covariant
Galileon type. The constraints arising from stability, the equivalence
principle and the constancy of fundamental constants are detailed and a
phenomenological picture of the emergence of the Lorentzian metric is
also given. The construction, while restricted to classical fields in
this article, offers a new view on the notion of time.


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Last-modified: 2013-11-20 (水) 11:11:56 (2067d)