88 research outputs found
CP Violation Makes Left-Right Symmetric Extensions With Non-Hermitian Mass Matrices Appear Unnatural
Following a similar recent analysis for CP violation in the electroweak
sector of the standard model, we estimate the naturalness of a magnitude of CP
violation (measured by the Jarlskog invariant J) close to the observed value in
extensions of the standard model with left-right symmetry, such as the
Pati-Salam model, where quark mass matrices are not Hermitian in general. We
construct a simple and natural measure on the space of complex matrices which
is both geometrically motivated and uses the observed quark mass hierarchy. We
find that, unlike in the case of the standard model where the observed value
for J seemed rather typical, one would now expect to observe |J|< 10^{-7},
clearly in conflict with the observed value J 3 x 10^{-5}. The
crucial difference in the calculation lies in the non-Hermiticity of mass
matrices that modifies the measure. We conclude that one would need additional
assumptions modifying the measure to reproduce the observed value, and that in
this sense the standard model is preferred to certain classes of left-right
symmetric extensions: It does not need additional assumptions to explain the
magnitude of CP violation.Comment: 17 pages, corrected minor typos, version to appear in Phys. Rev.
Classical general relativity as BF-Plebanski theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained BF theory, in the spirit of the Plebanski formulation, but
involving only linear constraints, of the type used recently in the spin foam
approach to quantum gravity. We identify both the continuum version of the
linear simplicity constraints used in the quantum discrete context and a linear
version of the quadratic volume constraints that are necessary to complete the
reduction from the topological theory to gravity. We illustrate and discuss
also the discrete counterpart of the same continuum linear constraints.
Moreover, we show under which additional conditions the discrete volume
constraints follow from the simplicity constraints, thus playing the role of
secondary constraints.Comment: 16 pages, revtex, changed one cross-reference in sect. IIIC to match
journal versio
Linking Covariant and Canonical General Relativity via Local Observers
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure
spacetime symmetries. We present an alternative, manifestly spacetime covariant
formulation that nonetheless distinguishes between "spatial" and "temporal"
variables. The key is viewing dynamical fields from the perspective of a field
of observers -- a unit timelike vector field that also transforms under local
Lorentz transformations. On one hand, all fields are spacetime fields,
covariant under spacetime symmeties. On the other, when the observer field is
normal to a spatial foliation, the fields automatically fall into Hamiltonian
form, recovering the Ashtekar formulation. We argue this provides a bridge
between Ashtekar variables and covariant phase space methods. We also outline a
framework where the 'space of observers' is fundamental, and spacetime geometry
itself may be observer-dependent.Comment: 8 pages; Essay written for the 2012 Gravity Research Foundation
Awards for Essays on Gravitatio
Two-point functions in (loop) quantum cosmology
The path-integral formulation of quantum cosmology with a massless scalar
field as a sum-over-histories of volume transitions is discussed, with
particular but non-exclusive reference to loop quantum cosmology. Exploiting
the analogy with the relativistic particle, we give a complete overview of the
possible two-point functions, pointing out the choices involved in their
definitions, deriving their vertex expansions and the composition laws they
satisfy. We clarify the origin and relations of different quantities previously
defined in the literature, in particular the tie between definitions using a
group averaging procedure and those in a deparametrized framework. Finally, we
draw some conclusions about the physics of a single quantum universe (where
there exist superselection rules on positive- and negative-frequency sectors
and different choices of inner product are physically equivalent) and
multiverse field theories where the role of these sectors and the inner product
are reinterpreted.Comment: 29 pages; v2: typos corrected, references adde
Quantum Cosmology
Invited contribution to the Encyclopedia of Mathematical Physics (2nd
edition), providing an overview over some main ideas and results in quantum
cosmology. Key points: Canonical quantisation of homogeneous, isotropic
cosmology; discussion of ambiguities in this quantisation; Construction of
explicit solutions, attempts at physical interpretation; conceptual issues
(time evolution, unitarity, probability interpretation); Introduction of scalar
fields or perfect fluids; Discussion of whether classical singularities are
resolved; Addition of inhomogeneities, possible predictions for primordial
cosmology; Connections to string theory and loop quantum gravity.Comment: Review article, 21 pages. To be published by Elsevier in the
Encyclopedia of Mathematical Physics (2nd edition
Classical GR as a topological theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained topological (BF) theory, in the spirit of the Plebanski
formulation, but involving only linear constraints, of the type used recently
in the spin foam approach to quantum gravity. We identify both the continuum
version of the linear simplicity constraints used in the quantum discrete
context and a linear version of the quadratic volume constraints that are
necessary to complete the reduction from the topological theory to gravity. We
illustrate and discuss also the discrete counterpart of the same continuum
linear constraints. Moreover, we show under which additional conditions the
discrete volume constraints follow from the simplicity constraints, thus
playing the role of secondary constraints. Our analysis clarifies how the
discrete constructions of spin foam models are related to a continuum theory
with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010
(ERE2010, Granada, Spain
Classical GR as a topological theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained topological (BF) theory, in the spirit of the Plebanski
formulation, but involving only linear constraints, of the type used recently
in the spin foam approach to quantum gravity. We identify both the continuum
version of the linear simplicity constraints used in the quantum discrete
context and a linear version of the quadratic volume constraints that are
necessary to complete the reduction from the topological theory to gravity. We
illustrate and discuss also the discrete counterpart of the same continuum
linear constraints. Moreover, we show under which additional conditions the
discrete volume constraints follow from the simplicity constraints, thus
playing the role of secondary constraints. Our analysis clarifies how the
discrete constructions of spin foam models are related to a continuum theory
with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010
(ERE2010, Granada, Spain
Classical GR as a topological theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained topological (BF) theory, in the spirit of the Plebanski
formulation, but involving only linear constraints, of the type used recently
in the spin foam approach to quantum gravity. We identify both the continuum
version of the linear simplicity constraints used in the quantum discrete
context and a linear version of the quadratic volume constraints that are
necessary to complete the reduction from the topological theory to gravity. We
illustrate and discuss also the discrete counterpart of the same continuum
linear constraints. Moreover, we show under which additional conditions the
discrete volume constraints follow from the simplicity constraints, thus
playing the role of secondary constraints. Our analysis clarifies how the
discrete constructions of spin foam models are related to a continuum theory
with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010
(ERE2010, Granada, Spain
Geometric aspects of gauge and spacetime symmetries
We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with symmetries in gravity. We apply the theory of Lie group deformations to isometry groups of exact solutions in general relativity, relating the algebraic properties of these groups to physical properties of the spacetimes. We then make group deformation local, generalising deformed special relativity (DSR) by describing gravity as a gauge theory of the de Sitter group. We find that in our construction Minkowski space has a connection with torsion; physical effects of torsion seem to rule out the proposed framework as a viable theory. A third chapter discusses a formulation of gravity as a topological BF theory with added linear constraints that reduce the symmetries of the topological theory to those of general relativity. We discretise our constructions and compare to a similar construction by Plebanski which uses quadratic constraints. In the second part we study CP violation in the electroweak sector of the standard model and certain extensions of it. We quantify fine-tuning in the observed magnitude of CP violation by determining a natural measure on the space of CKM matrices, a double quotient of SU(3), introducing different possible choices and comparing their predictions for CP violation. While one generically faces a fine-tuning problem, in the standard model the problem is removed by a measure that incorporates the observed quark masses, which suggests a close relation between a mass hierarchy and suppression of CP violation. Going beyond the standard model by adding a left-right symmetry spoils the result, leaving us to conclude that such additional symmetries appear less natural
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