82 research outputs found
Correlation experiments in nonlinear quantum mechanics
We show how one can compute multiple-time multi-particle correlation
functions in nonlinear quantum mechanics in a way which guarantees locality of
the formalism.Comment: Section on causally related corelation experiments is added (Russian
roulette with a cheating player as an analogue of nonlinear EPR problem); to
be published in Phys. Lett. A 301 (2002) 139-15
Anyons and the Bose-Fermi duality in the finite-temperature Thirring model
Solutions to the Thirring model are constructed in the framework of algebraic
QFT. It is shown that for all positive temperatures there are fermionic
solutions only if the coupling constant is . These fermions are inequivalent and only for they are canonical
fields. In the general case solutions are anyons. Different anyons (which are
uncountably many) live in orthogonal spaces and obey dynamical equations (of
the type of Heisenberg's "Urgleichung") characterized by the corresponding
values of the statistic parameter. Thus statistic parameter turns out to be
related to the coupling constant and the whole Hilbert space becomes
non-separable with a different "Urgleichung" satisfied in each of its sectors.
This feature certainly cannot be seen by any power expansion in .
Moreover, since the latter is tied to the statistic parameter, it is clear that
such an expansion is doomed to failure and will never reveal the true structure
of the theory.
The correlation functions in the temperature state for the canonical dressed
fermions are shown by us to coincide with the ones for bare fields, that is in
agreement with the uniqueness of the -KMS state over the CAR algebra
( being the shift automorphism). Also the -anyon two-point
function is evaluated and for scalar field it reproduces the result that is
known from the literature.Comment: 25 pages, LaTe
Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
The superselection sectors of two classes of scalar bilocal quantum fields in
D>=4 dimensions are explicitly determined by working out the constraints
imposed by unitarity. The resulting classification in terms of the dual of the
respective gauge groups U(N) and O(N) confirms the expectations based on
general results obtained in the framework of local nets in algebraic quantum
field theory, but the approach using standard Lie algebra methods rather than
abstract duality theory is complementary. The result indicates that one does
not lose interesting models if one postulates the absence of scalar fields of
dimension D-2 in models with global conformal invariance. Another remarkable
outcome is the observation that, with an appropriate choice of the Hamiltonian,
a Lie algebra embedded into the associative algebra of observables completely
fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio
Geometrization of Quantum Mechanics
We show that it is possible to represent various descriptions of Quantum
Mechanics in geometrical terms. In particular we start with the space of
observables and use the momentum map associated with the unitary group to
provide an unified geometrical description for the different pictures of
Quantum Mechanics. This construction provides an alternative to the usual GNS
construction for pure states.Comment: 16 pages. To appear in Theor. Math. Phys. Some typos corrected.
Definition 2 in page 5 rewritte
Nonlocal looking equations can make nonlinear quantum dynamics local
A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition is fulfilled. It is shown that a correct
extension to particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.Comment: revtex, final version, accepted in Phys.Rev.A (June 1998
An alternative to the gauge theoretic setting
The standard formulation of gauge theories results from the Lagrangian
(functional integral) quantization of classical gauge theories. A more
intrinsic qunantum theoretical access in the spirit of Wigner's representation
theory shows that there is a fundamental clash between the pointlike
localization of zero mass (vector, tensor) potentials and the Hilbert space
(positivity, unitarity) structure of QT. The quantization approach has no other
way than to stay with pointlike localization and sacrifice the Hilbert space
whereas the approach build on the intrinsic quantum concept of modular
localization keeps the Hilbert space and trades the conflict creating pointlike
generation with the tightest consistent localization:: semiinfinite spacelike
string localization. Whereas these potentials in the presence of interactions
stay quite close to associated pointlike field strength, the interacting matter
fields to which they are coupled bear the brunt of the nonlocal aspect in that
they are string.generated in a way which cannot be undone by any
differentiation. The new stringlike approach to gauge theory also revives the
idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric
description of the Higgs spontaneous symmetry breaking and its accompanying
tale about "God's particle" and its mass generation for all other particles.Comment: 26 page
String-localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with
irreducible representations of the Poincar\'e group and localized in
semi-infinite strings extending to spacelike infinity. Among these are fields
that generate the irreducible representations of mass zero and infinite spin
that are known to be incompatible with point-like localized fields. For the
massive representation and the massless representations of finite helicity, all
string-localized free fields can be written as an integral, along the string,
of point-localized tensor or spinor fields. As a special case we discuss the
string-localized vector fields associated with the point-like electromagnetic
field and their relation to the axial gauge condition in the usual setting.Comment: minor correction
Complete positivity of nonlinear evolution: A case study
Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection
postulate, nonlocality), to be published in Phys. Rev.
Stochastic dynamics of correlations in quantum field theory: From Schwinger-Dyson to Boltzmann-Langevin equation
The aim of this paper is two-fold: in probing the statistical mechanical
properties of interacting quantum fields, and in providing a field theoretical
justification for a stochastic source term in the Boltzmann equation. We start
with the formulation of quantum field theory in terms of the Schwinger - Dyson
equations for the correlation functions, which we describe by a
closed-time-path master () effective action. When the hierarchy
is truncated, one obtains the ordinary closed-system of correlation functions
up to a certain order, and from the nPI effective action, a set of
time-reversal invariant equations of motion. But when the effect of the higher
order correlation functions is included (through e.g., causal factorization--
molecular chaos -- conditions, which we call 'slaving'), in the form of a
correlation noise, the dynamics of the lower order correlations shows
dissipative features, as familiar in the field-theory version of Boltzmann
equation. We show that fluctuation-dissipation relations exist for such
effectively open systems, and use them to show that such a stochastic term,
which explicitly introduces quantum fluctuations on the lower order correlation
functions, necessarily accompanies the dissipative term, thus leading to a
Boltzmann-Langevin equation which depicts both the dissipative and stochastic
dynamics of correlation functions in quantum field theory.Comment: LATEX, 30 pages, no figure
Critical mutation rate has an exponential dependence on population size for eukaryotic-length genomes with crossover
The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction
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