629,131 research outputs found
Real-time propagators at finite temperature and chemical potential
We derive a form of spectral representations for all bosonic and fermionic
propagators in the real-time formulation of field theory at finite temperature
and chemical potential. Besides being simple and symmetrical between the
bosonic and the fermionic types, these representations depend explicitly on
analytic functions only. This last property allows a simple evaluation of loop
integrals in the energy variables over propagators in this form, even in
presence of chemical potentials, which is not possible over their conventional
form
New knotted solutions of Maxwell's equations
In this note we have further developed the study of topologically non-trivial
solutions of vacuum electrodynamics. We have discovered a novel method of
generating such solutions by applying conformal transformations with complex
parameters on known solutions expressed in terms of Bateman's variables. This
has enabled us to get a wide class of solutions from the basic configuration
like constant electromagnetic fields and plane-waves. We have introduced a
covariant formulation of the Bateman's construction and discussed the conserved
charges associated with the conformal group as well as a set of four types of
conserved helicities. We have also given a formulation in terms of quaternions.
This led to a simple map between the electromagnetic knotted and linked
solutions into flat connections of gauge theory. We have computed the
corresponding CS charge in a class of solutions and it takes integer values.Comment: version accepted for publication in J. Phys. A. minor changes:
references added, new figure added, typos correcte
Bosons, fermions and anyons in the plane, and supersymmetry
Universal vector wave equations allowing for a unified description of anyons,
and also of usual bosons and fermions in the plane are proposed. The existence
of two essentially different types of anyons, based on unitary and also on
non-unitary infinite-dimensional half-bounded representations of the (2+1)D
Lorentz algebra is revealed. Those associated with non-unitary representations
interpolate between bosons and fermions. The extended formulation of the theory
includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD)
descriptions of anyons as particular cases, and allows us to compose bosons and
fermions from entangled anyons. The theory admits a simple supersymmetric
generalization, in which the JN and MD systems are unified in N=1 and N=2
supermultiplets. Two different non-relativistic limits of the theory are
investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to
arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that
corresponds to Inonu-Wigner contraction with both anyon spin and light velocity
going to infinity), is generalized to boson/fermion fields and interpolating
anyons. The resulting exotic Galilei symmetry is studied in both the
non-supersymmetric and the supersymmetric cases.Comment: 54 pages. Typos corrected, refs updated. Published versio
Greatest HITs: Higher Inductive Types in Coinductive Definitions via Induction under Clocks
Guarded recursion is a powerful modal approach to recursion that can be seen
as an abstract form of step-indexing. It is currently used extensively in
separation logic to model programming languages with advanced features by
solving domain equations also with negative occurrences. In its multi-clocked
version, guarded recursion can also be used to program with and reason about
coinductive types, encoding the productivity condition required for recursive
definitions in types. This paper presents the first type theory combining
multi-clocked guarded recursion with the features of Cubical Type Theory, as
well as a denotational semantics. Using the combination of Higher Inductive
Types (HITs) and guarded recursion allows for simple programming and reasoning
about coinductive types that are traditionally hard to represent in type
theory, such as the type of finitely branching labelled transition systems. For
example, our results imply that bisimilarity for these imply path equality, and
so proofs can be transported along bisimilarity proofs. Among our technical
contributions is a new principle of induction under clocks. This allows
universal quantification over clocks to commute with HITs up to equivalence of
types, and is crucial for the encoding of coinductive types. Such commutativity
requirements have been formulated for inductive types as axioms in previous
type theories with multi-clocked guarded recursion, but our present formulation
as an induction principle allows for the formulation of general computation
rules.Comment: 29 page
Inflation, Symmetry, and B-Modes
We examine the role of using symmetry and effective field theory in
inflationary model building. We describe the standard formulation of starting
with an approximate shift symmetry for a scalar field, and then introducing
corrections systematically in order to maintain control over the inflationary
potential. We find that this leads to models in good agreement with recent
data. On the other hand, there are attempts in the literature to deviate from
this paradigm by invoking other symmetries and corrections. In particular: in a
suite of recent papers, several authors have made the claim that standard
Einstein gravity with a cosmological constant and a massless scalar carries
conformal symmetry. They further claim that such a theory carries another
hidden symmetry; a global SO(1,1) symmetry. By deforming around the global
SO(1,1) symmetry, they are able to produce a range of inflationary models with
asymptotically flat potentials, whose flatness is claimed to be protected by
these symmetries. These models tend to give rise to B-modes with small
amplitude. Here we explain that these authors are merely introducing a
redundancy into the description, not an actual conformal symmetry. Furthermore,
we explain that the only real (global) symmetry in these models is not at all
hidden, but is completely manifest when expressed in the Einstein frame; it is
in fact the shift symmetry of a scalar field. When analyzed systematically as
an effective field theory, deformations do not generally produce asymptotically
flat potentials and small B-modes, but other types of potentials with B-modes
of appreciable amplitude. Such simple models typically also produce the
observed red spectral index, Gaussian fluctuations, etc. In short: simple
models of inflation, organized by expanding around a shift symmetry, are in
excellent agreement with recent data.Comment: 9 pages in double column format. V2: Updated to coincide with version
published in Physics Letters
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