345 research outputs found
Volume Dependence of Spectral Weights for Unstable Particles in a Solvable Model
Volume dependence of the spectral weight is usually used as a simple criteria
to distinguish single-particle states from multi-particle states in lattice QCD
calculations. Within a solvable model, the Lee model, we show that this
criteria is in principle only valid for a stable particle or a narrow
resonance. If the resonance being studied is broad, then the volume dependence
of the corresponding spectral weight resembles that of a multi-particle state
instead of a single-particle one. For an unstable -particle in the Lee
model, the transition from single-particle to multi-particle volume dependence
is governed by the ratio of its physical width to the typical level spacing in
the finite volume. We estimate this ratio for practical lattice QCD simulations
and find that, for most cases, the resonance studied in lattice QCD simulations
still resembles the single particle behavior.Comment: 15 pages, no figures. Title modified. Version to appear on Phys. Rev.
3-dimensional Rules for Finite-Temperature Loops
We present simple diagrammatic rules to write down Euclidean n-point
functions at finite temperature directly in terms of 3-dimensional momentum
integrals, without ever performing a single Matsubara sum. The rules can be
understood as describing the interaction of the external particles with those
of the thermal bath.Comment: 12 pages, 4 figures, to appear in Physics Letters
Quantum electrodynamics of relativistic bound states with cutoffs
We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing
the interaction of relativistic electrons and positrons in the Coulomb
potential with photons in Coulomb gauge. The interaction includes both
interaction of the current density with transversal photons and the Coulomb
interaction of charge density with itself. We prove that the Hamiltonian is
self-adjoint and has a ground state for sufficiently small coupling constants.Comment: To appear in "Journal of Hyperbolic Differential Equation
Relating on-shell and off-shell formalism in perturbative quantum field theory
In the on-shell formalism (mostly used in perturbative quantum field theory)
the entries of the time ordered product T are on-shell fields (i.e. the basic
fields satisfy the free field equations). With that, (multi)linearity of T is
incompatible with the Action Ward identity. This can be circumvented by using
the off-shell formalism in which the entries of T are off-shell fields. To
relate on- and off-shell formalism correctly, a map sigma from on-shell fields
to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In
that paper it was shown that, in the case of one real scalar field in N=4
dimensional Minkowski space, these axioms have a unique solution. However, this
solution was given there only recursively. We solve this recurrence relation
and give a fully explicit expression for sigma in the cases of the scalar,
Dirac and gauge fields for arbitrary values of the dimension N.Comment: The case of gauge fields was added. 16 page
Moving system with speeded-up evolution
In the classical (non-quantum) relativity theory the course of the moving
clock is dilated as compared to the course of the clock at rest (the Einstein
dilation). Any unstable system may be regarded as a clock. The time evolution
(e.g., the decay) of a uniformly moving physical system is considered using the
relativistic quantum theory. The example of a moving system is given whose
evolution turns out to be speeded-up instead of being dilated. A discussion of
this paradoxical result is presented.Comment: 10 pages, LaTe
Renormalized Electron Mass in Nonrelativistic QED
Within the framework of nonrelativistic QED, we prove that, for small values
of the coupling constant, the energy function, E_|P|, of a dressed electron is
twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore,
(E_|P|)" is bounded from below by a constant larger than zero. Our results are
proven with the help of iterative analytic perturbation theory
Time-of-arrival formalism for the relativistic particle
A suitable operator for the time-of-arrival at a detector is defined for the
free relativistic particle in 3+1 dimensions. For each detector position, there
exists a subspace of detected states in the Hilbert space of solutions to the
Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of
the time-of-arrival operator apply inside this subspace, opening up a standard
probabilistic interpretation.Comment: 16 pages, no figures, uses LaTeX. The section "Interpretation" has
been completely rewritten and some errors correcte
The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds
A new approach to the concept of particles and their production in quantum
field theory is developed. A local operator describing the current of particle
density is constructed for scalar and spinor fields in arbitrary gravitational
and electromagnetic backgrounds. This enables one to describe particles in a
local, general-covariant and gauge-invariant way. However, the current depends
on the choice of a 2-point function. There is a choice that leads to the local
non-conservation of the current in a gravitational or an electromagnetic
background, which describes local particle production consistent with the usual
global description based on the Bogoliubov transformation. The most natural
choice based on the Green function calculated using the Schwinger-DeWitt method
leads to the local conservation of the current, provided that interactions with
quantum fields are absent. Interactions with quantum fields lead to the local
non-conservation of the current which describes local particle production
consistent with the usual global description based on the interaction picture.Comment: 34 pages, revised, to appear in Int. J. Mod. Phys.
Trajectories and Particle Creation and Annihilation in Quantum Field Theory
We develop a theory based on Bohmian mechanics in which particle world lines
can begin and end. Such a theory provides a realist description of creation and
annihilation events and thus a further step towards a "beable-based"
formulation of quantum field theory, as opposed to the usual "observable-based"
formulation which is plagued by the conceptual difficulties--like the
measurement problem--of quantum mechanics.Comment: 11 pages LaTeX, no figures; v2: references added and update
Relativistic Lee Model on Riemannian Manifolds
We study the relativistic Lee model on static Riemannian manifolds. The model
is constructed nonperturbatively through its resolvent, which is based on the
so-called principal operator and the heat kernel techniques. It is shown that
making the principal operator well-defined dictates how to renormalize the
parameters of the model. The renormalization of the parameters are the same in
the light front coordinates as in the instant form. Moreover, the
renormalization of the model on Riemannian manifolds agrees with the flat case.
The asymptotic behavior of the renormalized principal operator in the large
number of bosons limit implies that the ground state energy is positive. In 2+1
dimensions, the model requires only a mass renormalization. We obtain rigorous
bounds on the ground state energy for the n-particle sector of 2+1 dimensional
model.Comment: 23 pages, added a new section, corrected typos and slightly different
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