1,371 research outputs found
Dynamical mapping method in nonrelativistic models of quantum field theory
The solutions of Heisenberg equations and two-particles eigenvalue problems
for nonrelativistic models of current-current fermion interaction and model are obtained in the frameworks of dynamical mapping method. The
equivalence of different types of dynamical mapping is shown. The connection
between renormalization procedure and theory of selfadjoint extensions is
elucidated.Comment: 14 page
Non Local Theories: New Rules for Old Diagrams
We show that a general variant of the Wick theorems can be used to reduce the
time ordered products in the Gell-Mann & Low formula for a certain class on non
local quantum field theories, including the case where the interaction
Lagrangian is defined in terms of twisted products.
The only necessary modification is the replacement of the
Stueckelberg-Feynman propagator by the general propagator (the ``contractor''
of Denk and Schweda)
D(y-y';tau-tau')= - i
(Delta_+(y-y')theta(tau-tau')+Delta_+(y'-y)theta(tau'-tau)), where the
violations of locality and causality are represented by the dependence of
tau,tau' on other points, besides those involved in the contraction. This leads
naturally to a diagrammatic expansion of the Gell-Mann & Low formula, in terms
of the same diagrams as in the local case, the only necessary modification
concerning the Feynman rules. The ordinary local theory is easily recovered as
a special case, and there is a one-to-one correspondence between the local and
non local contributions corresponding to the same diagrams, which is preserved
while performing the large scale limit of the theory.Comment: LaTeX, 14 pages, 1 figure. Uses hyperref. Symmetry factors added;
minor changes in the expositio
Thermodynamic Limit and Decoherence: Rigorous Results
Time evolution operator in quantum mechanics can be changed into a
statistical operator by a Wick rotation. This strict relation between
statistical mechanics and quantum evolution can reveal deep results when the
thermodynamic limit is considered. These results translate in a set of theorems
proving that these effects can be effectively at work producing an emerging
classical world without recurring to any external entity that in some cases
cannot be properly defined. In a many-body system has been recently shown that
Gaussian decay of the coherence is the rule with a duration of recurrence more
and more small as the number of particles increases. This effect has been
observed experimentally. More generally, a theorem about coherence of bulk
matter can be proved. All this takes us to the conclusion that a well definite
boundary for the quantum to classical world does exist and that can be drawn by
the thermodynamic limit, extending in this way the deep link between
statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006
(Piombino, Italy, September 11-15, 2006
Haag-Ruelle scattering theory in presence of massless particles
Within the framework of local quantum physics we construct a scattering
theory of stable, massive particles without assuming mass gaps. This extension
of the Haag-Ruelle theory is based on advances in the harmonic analysis of
local operators. Our construction is restricted to theories complying with a
regularity property introduced by Herbst. The paper concludes with a brief
discussion of the status of this assumption.Comment: As appeared in Letters in Mathematical Physic
Quantum control without access to the controlling interaction
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum
system and its controller. We show under which conditions measurements, state
preparations, and unitary implementations on the system can be performed by
quantum operations on the controller only.
It turns out that a measurement of the observable A and an implementation of
the one-parameter group exp(iAr) can be performed by almost the same sequence
of control operations. Furthermore measurement procedures for A+B, for (AB+BA),
and for i[A,B] can be constructed from measurements of A and B. This shows that
the algebraic structure of the set of observables can be explained by the Lie
group structure of the unitary evolutions on the joint Hilbert space of the
measuring device and the measured system.
A spin chain model with nearest neighborhood coupling shows that the border
line between controller and system can be shifted consistently.Comment: 10 pages, Revte
Curie-Weiss model of the quantum measurement process
A hamiltonian model is solved, which satisfies all requirements for a
realistic ideal quantum measurement. The system S is a spin-\half, whose
-component is measured through coupling with an apparatus A=M+B, consisting
of a magnet \RM formed by a set of spins with quartic infinite-range
Ising interactions, and a phonon bath \RB at temperature . Initially A is
in a metastable paramagnetic phase. The process involves several time-scales.
Without being much affected, A first acts on S, whose state collapses in a very
brief time. The mechanism differs from the usual decoherence. Soon after its
irreversibility is achieved. Finally the field induced by S on M, which may
take two opposite values with probabilities given by Born's rule, drives A into
its up or down ferromagnetic phase. The overall final state involves the
expected correlations between the result registered in M and the state of S.
The measurement is thus accounted for by standard quantum statistical mechanics
and its specific features arise from the macroscopic size of the apparatus.Comment: 5 pages Revte
Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of field theory
In this paper we study the renormalization of the Schwinger-Dyson equations
that arise in the auxiliary field formulation of the O(N) field
theory. The auxiliary field formulation allows a simple interpretation of the
large-N expansion as a loop expansion of the generating functional in the
auxiliary field , once the effective action is obtained by integrating
over the fields. Our all orders result is then used to obtain finite
renormalized Schwinger-Dyson equations based on truncation expansions which
utilize the two-particle irreducible (2-PI) generating function formalism. We
first do an all orders renormalization of the two- and three-point function
equations in the vacuum sector. This result is then used to obtain explicitly
finite and renormalization constant independent self-consistent S-D equations
valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for
the real and imaginary parts of the renormalized Green's functions with the
related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees
and Knoll, and comment on the importance of the Landau pole effect.Comment: 20 pages, 10 figure
Master integrals for massive two-loop Bhabha scattering in QED
We present a set of scalar master integrals (MIs) needed for a complete
treatment of massive two-loop corrections to Bhabha scattering in QED,
including integrals with arbitrary fermionic loops. The status of analytical
solutions for the MIs is reviewed and examples of some methods to solve MIs
analytically are worked out in more detail. Analytical results for the pole
terms in epsilon of so far unknown box MIs with five internal lines are given.Comment: 23 pages, 5 tables, 12 figures, references added, appendix B enlarge
Wedge-Local Quantum Fields and Noncommutative Minkowski Space
Within the setting of a recently proposed model of quantum fields on
noncommutative Minkowski spacetime, the consequences of the consistent
application of the proper, untwisted Poincare group as the symmetry group are
investigated. The emergent model contains an infinite family of fields which
are labelled by different noncommutativity parameters, and related to each
other by Lorentz transformations. The relative localization properties of these
fields are investigated, and it is shown that to each field one can assign a
wedge-shaped localization region of Minkowski space. This assignment is
consistent with the principles of covariance and locality, i.e. fields
localized in spacelike separated wedges commute.
Regarding the model as a non-local, but wedge-local, quantum field theory on
ordinary (commutative) Minkowski spacetime, it is possible to determine
two-particle S-matrix elements, which turn out to be non-trivial. Some partial
negative results concerning the existence of observables with sharper
localization properties are also obtained.Comment: Version to appear in JHEP, 27 page
Quantum measurements without macroscopic superpositions
We study a class of quantum measurement models. A microscopic object is
entangled with a macroscopic pointer such that each eigenvalue of the measured
object observable is tied up with a specific pointer deflection. Different
pointer positions mutually decohere under the influence of a bath.
Object-pointer entanglement and decoherence of distinct pointer readouts
proceed simultaneously. Mixtures of macroscopically distinct object-pointer
states may then arise without intervening macroscopic superpositions.
Initially, object and apparatus are statistically independent while the latter
has pointer and bath correlated according to a metastable local thermal
equilibrium. We obtain explicit results for the object-pointer dynamics with
temporal coherence decay in general neither exponential nor Gaussian. The
decoherence time does not depend on details of the pointer-bath coupling if it
is smaller than the bath correlation time, whereas in the opposite Markov
regime the decay depends strongly on whether that coupling is Ohmic or
super-Ohmic.Comment: 50 pages, 5 figures, changed conten
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