12,117 research outputs found
Two Notions of Naturalness
My aim in this paper is twofold: (i) to distinguish two notions of
naturalness employed in BSM physics and (ii) to argue that recognizing this
distinction has methodological consequences. One notion of naturalness is an
"autonomy of scales" requirement: it prohibits sensitive dependence of an
effective field theory's low-energy observables on precise specification of the
theory's description of cutoff-scale physics. I will argue that considerations
from the general structure of effective field theory provide justification for
the role this notion of naturalness has played in BSM model construction. A
second, distinct notion construes naturalness as a statistical principle
requiring that the values of the parameters in an effective field theory be
"likely" given some appropriately chosen measure on some appropriately
circumscribed space of models. I argue that these two notions are historically
and conceptually related but are motivated by distinct theoretical
considerations and admit of distinct kinds of solution.Comment: 34 pages, 1 figur
Canonical Gravity, Diffeomorphisms and Objective Histories
This paper discusses the implementation of diffeomorphism invariance in
purely Hamiltonian formulations of General Relativity. We observe that, if a
constrained Hamiltonian formulation derives from a manifestly covariant
Lagrangian, the diffeomorphism invariance of the Lagrangian results in the
following properties of the constrained Hamiltonian theory: the diffeomorphisms
are generated by constraints on the phase space so that a) The algebra of the
generators reflects the algebra of the diffeomorphism group. b) The Poisson
brackets of the basic fields with the generators reflects the space-time
transformation properties of these basic fields. This suggests that in a purely
Hamiltonian approach the requirement of diffeomorphism invariance should be
interpreted to include b) and not just a) as one might naively suppose. Giving
up b) amounts to giving up objective histories, even at the classical level.
This observation has implications for Loop Quantum Gravity which are spelled
out in a companion paper. We also describe an analogy between canonical gravity
and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees'
comments, accepted for publication in Classical and Quantum Gravit
Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model
In this letter we explore different representations of the SU(2) principal
chiral model on the lattice. We couple chemical potentials to two of the
conserved charges to induce finite density. This leads to a complex action such
that the conventional field representation cannot be used for a Monte Carlo
simulation. Using the recently developed Abelian color flux approach we derive
a new worldline representation where the partition sum has only real and
positive weights, such that a Monte Carlo simulation is possible. In a second
step we transform the model to new dual variables in the Kramers-Wannier (KW)
sense, such that the constraints are automatically fulfilled, and we obtain a
second representation free of the complex action problem. We implement
exploratory Monte Carlo simulations for both, the worldline, as well as the
KW-dual form, for cross-checking the two dualizations and a first assessment of
their potential for dual simulations.Comment: Comments and a new plot for the relative errors added. Version to
appear in Physics Letters
Superspace Formulation of 4D Higher Spin Gauge Theory
Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so
far have been formulated as constrained systems of differential forms living in
a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory
in superspace, leaving the internal twistor space intact. Remarkably, the
superspace constraints have the same form as those defining the theory in
ordinary spacetime. This construction generalizes straightforwardly to higher
spin gauge theories N>1 supersymmetry.Comment: 24 p
The Stueckelberg Field
In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge
theory massive but preserves gauge invariance. The Stueckelberg mechanism is
the introduction of new fields to reveal a symmetry of a gauge--fixed theory.
We first review the Stueckelberg mechanism in the massive Abelian gauge theory.
We then extend this idea to the standard model, stueckelberging the
hypercharge U(1) and thus giving a mass to the physical photon. This introduces
an infrared regulator for the photon in the standard electroweak theory, along
with a modification of the weak mixing angle accompanied by a plethora of new
effects. Notably, neutrinos couple to the photon and charged leptons have also
a pseudo-vector coupling. Finally, we review the historical influence of
Stueckelberg's 1938 idea, which led to applications in many areas not
anticipated by the author, such as strings. We describe the numerous proposals
to generalize the Stueckelberg trick to the non-Abelian case with the aim to
find alternatives to the standard model. Nevertheless, the Higgs mechanism in
spontaneous symmetry breaking remains the only presently known way to give
masses to non-Abelian vector fields in a renormalizable and unitary theory.Comment: 58 pages, revtex4 RMP format. Added references, minor improvements to
tex
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