1,420 research outputs found
Reeh-Schlieder Defeats Newton-Wigner: On alternative localization schemes in relativistic quantum field theory
Many of the "counterintuitive" features of relativistic quantum field theory
have their formal root in the Reeh-Schlieder theorem, which in particular
entails that local operations applied to the vacuum state can produce any state
of the entire field. It is of great interest, then, that I.E. Segal and, more
recently, G. Fleming (in a paper entitled "Reeh-Schlieder Meets Newton-Wigner")
have proposed an alternative "Newton-Wigner" localization scheme that avoids
the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner
localization scheme and clarify the limited extent to which it avoids the
counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that
neither Segal nor Fleming has provided a coherent account of the physical
meaning of Newton-Wigner localization.Comment: 25 pages, LaTe
Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics
After recalling episodes from Pascual Jordan's biography including his
pivotal role in the shaping of quantum field theory and his much criticized
conduct during the NS regime, I draw attention to his presentation of the first
phase of development of quantum field theory in a talk presented at the 1929
Kharkov conference. He starts by giving a comprehensive account of the
beginnings of quantum theory, emphasising that particle-like properties arise
as a consequence of treating wave-motions quantum-mechanically. He then goes on
to his recent discovery of quantization of ``wave fields'' and problems of
gauge invariance. The most surprising aspect of Jordan's presentation is
however his strong belief that his field quantization is a transitory not yet
optimal formulation of the principles underlying causal, local quantum physics.
The expectation of a future more radical change coming from the main architect
of field quantization already shortly after his discovery is certainly quite
startling. I try to answer the question to what extent Jordan's 1929
expectations have been vindicated. The larger part of the present essay
consists in arguing that Jordan's plea for a formulation without ``classical
correspondence crutches'', i.e. for an intrinsic approach (which avoids
classical fields altogether), is successfully addressed in past and recent
publications on local quantum physics.Comment: More biographical detail, expansion of the part referring to Jordan's
legacy in quantum field theory, 37 pages late
The Bond-Algebraic Approach to Dualities
An algebraic theory of dualities is developed based on the notion of bond
algebras. It deals with classical and quantum dualities in a unified fashion
explaining the precise connection between quantum dualities and the low
temperature (strong-coupling)/high temperature (weak-coupling) dualities of
classical statistical mechanics (or (Euclidean) path integrals). Its range of
applications includes discrete lattice, continuum field, and gauge theories.
Dualities are revealed to be local, structure-preserving mappings between
model-specific bond algebras that can be implemented as unitary
transformations, or partial isometries if gauge symmetries are involved. This
characterization permits to search systematically for dualities and
self-dualities in quantum models of arbitrary system size, dimensionality and
complexity, and any classical model admitting a transfer matrix representation.
Dualities like exact dimensional reduction, emergent, and gauge-reducing
dualities that solve gauge constraints can be easily understood in terms of
mappings of bond algebras. As a new example, we show that the (\mathbb{Z}_2)
Higgs model is dual to the extended toric code model {\it in any number of
dimensions}. Non-local dual variables and Jordan-Wigner dictionaries are
derived from the local mappings of bond algebras. Our bond-algebraic approach
goes beyond the standard approach to classical dualities, and could help
resolve the long standing problem of obtaining duality transformations for
lattice non-Abelian models. As an illustration, we present new dualities in any
spatial dimension for the quantum Heisenberg model. Finally, we discuss various
applications including location of phase boundaries, spectral behavior and,
notably, we show how bond-algebraic dualities help constrain and realize
fermionization in an arbitrary number of spatial dimensions.Comment: 131 pages, 22 figures. Submitted to Advances in Physics. Second
version including a new section on the eight-vertex model and the correction
of several typo
Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
Decoherence-free subspaces (DFSs) shield quantum information from errors
induced by the interaction with an uncontrollable environment. Here we study a
model of correlated errors forming an Abelian subgroup (stabilizer) of the
Pauli group (the group of tensor products of Pauli matrices). Unlike previous
studies of DFSs, this type of errors does not involve any spatial symmetry
assumptions on the system-environment interaction. We solve the problem of
universal, fault-tolerant quantum computation on the associated class of DFSs.Comment: 22 pages, 4 figures. Sequel to quant-ph/990806
Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
The search for strong topological phases in generic aperiodic materials and
meta-materials is now vigorously pursued by the condensed matter physics
community. In this work, we first introduce the concept of patterned resonators
as a unifying theoretical framework for topological electronic, photonic,
phononic etc. (aperiodic) systems. We then discuss, in physical terms, the
philosophy behind an operator theoretic analysis used to systematize such
systems. A model calculation of the Hall conductance of a 2-dimensional
amorphous lattice is given, where we present numerical evidence of its
quantization in the mobility gap regime. Motivated by such facts, we then
present the main result of our work, which is the extension of the Chern number
formulas to Hamiltonians associated to lattices without a canonical labeling of
the sites, together with index theorems that assure the quantization and
stability of these Chern numbers in the mobility gap regime. Our results cover
a broad range of applications, in particular, those involving
quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically
generated) lattices.Comment: 44 pages, 4 figures. v2: typos corrected and references updated. v3:
Minor changes, to appear in J. Phys. A (Mathematical and Theoretical
Schwinger-Keldysh formalism II: Thermal equivariant cohomology
Causally ordered correlation functions of local operators in near-thermal
quantum systems computed using the Schwinger-Keldysh formalism obey a set of
Ward identities. These can be understood rather simply as the consequence of a
topological (BRST) algebra, called the universal Schwinger-Keldysh
superalgebra, as explained in our companion paper arXiv:1610.01940. In the
present paper we provide a mathematical discussion of this topological algebra.
In particular, we argue that the structures can be understood in the language
of extended equivariant cohomology. To keep the discussion self-contained, we
provide a basic review of the algebraic construction of equivariant cohomology
and explain how it can be understood in familiar terms as a superspace gauge
algebra. We demonstrate how the Schwinger-Keldysh construction can be
succinctly encoded in terms a thermal equivariant cohomology algebra which
naturally acts on the operator (super)-algebra of the quantum system. The main
rationale behind this exploration is to extract symmetry statements which are
robust under renormalization group flow and can hence be used to understand
low-energy effective field theory of near-thermal physics. To illustrate the
general principles, we focus on Langevin dynamics of a Brownian particle,
rephrasing some known results in terms of thermal equivariant cohomology. As
described elsewhere, the general framework enables construction of effective
actions for dissipative hydrodynamics and could potentially illumine our
understanding of black holes.Comment: 72 pages; v2: fixed typos. v3: minor clarifications and improvements
to non-equilbirum work relations discussion. v4: typos fixed. published
versio
`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms
We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation
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