754 research outputs found

### Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity

The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Reâșeâ», the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly

### The Non-Trivial Effective Potential of the `Trivial' lambda Phi^4 Theory: A Lattice Test

The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not
incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory
the effective potential should be given exactly by the classical potential plus
the free-field zero-point energy of the shifted field; i.e., by the one-loop
effective potential. When this is renormalized in a simple, but nonperturbative
way, one finds, self-consistently, that the shifted field does become
non-interacting in the continuum limit. For a classically scale-invariant (CSI)
lambda Phi^4 theory one finds m_h^2 = 8 pi^2 v^2, predicting a 2.2 TeV Higgs
boson. Here we extend our earlier work in three ways: (i) we discuss the
analogy with the hard-sphere Bose gas; (ii) we extend the analysis from the CSI
case to the general case; and (iii) we propose a test of the predicted shape of
the effective potential that could be tested in a lattice simulation.Comment: 22 pages, LaTeX, DE-FG05-92ER40717-

### QCD perturbation theory at large orders with large renormalization scales in the large $\beta_0$ limit

We examine the QCD perturbation series at large orders, for different values
of the 'large $\beta_0$ renormalization scale'. It is found that if we let this
scale grow exponentially with the order, the divergent series can be turned
into an expansion that converges to the Borel integral, with a certain cut off.
In the case of the first IR renormalon at $2/\beta_0$, corresponding to a
dimension four operator in the operator product expansion, this qualitatively
improves the perturbative predictions. Furthermore, our results allow us to
establish formulations of the principle of minimal sensitivity and the fastest
apparent convergence criterion that result in a convergent expansion.Comment: 14 pages, 5 figures, elaborated conclusion

### Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

We show that in applications of variational theory to quantum field theory it
is essential to account for the correct Wegner exponent omega governing the
approach to the strong-coupling, or scaling limit. Otherwise the procedure
either does not converge at all or to the wrong limit. This invalidates all
papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/34

### On the Existence of the Quantum Action

We have previously proposed a conjecture stating that quantum mechanical
transition amplitudes can be parametrized in terms of a quantum action. Here we
give a proof of the conjecture and establish the existance of a local quantum
action in the case of imaginary time in the Feynman-Kac limit (when temperature
goes to zero). Moreover we discuss some symmetry properties of the quantum
action.Comment: revised version, Text (LaTeX

### A Variational Approach to Bound States in Quantum Field Theory

We consider here in a toy model an approach to bound state problem in a
nonperturbative manner using equal time algebra for the interacting field
operators. Potential is replaced by offshell bosonic quanta inside the bound
state of nonrelativistic particles. The bosonic dressing is determined through
energy minimisation, and mass renormalisation is carried out in a
nonperturbative manner. Since the interaction is through a scalar field, it
does not include spin effects. The model however nicely incorporates an
intuitive picture of hadronic bound states in which the gluon fields dress the
quarks providing the binding between them and also simulate the gluonic content
of hadrons in deep inelastic collisions.Comment: latex, revtex, 22 page

### QCD Corrections to t anti-b H^- Associated Production in e^+ e^- Annihilation

We calculate the QCD corrections to the cross section of e^+ e^- -> t anti-b
H^- and its charge-conjugate counterpart within the minimal supersymmetric
extension of the Standard Model. This process is particularly important if m_t
b H^+ and e^+ e^- -> H^+ H^- are
not allowed kinematically. Large logarithmic corrections that arise in the
on-mass-shell scheme of quark mass renormalization, especially from the t
anti-b H^- Yukawa coupling for large values of tan(beta), are resummed by
adopting the modified minimal-subtraction scheme, so that the convergence
behavior of the perturbative expansion is improved. The inclusion of the QCD
corrections leads to a significant reduction of the theoretical uncertainties
due to scheme and scale dependences.Comment: 21 pages (Latex), 8 figures (Postscript); detailed discussion of
scheme and scale dependences adde

### High-Order Variational Calculation for the Frequency of Time-Periodic Solutions

We develop a convergent variational perturbation theory for the frequency of
time-periodic solutions of nonlinear dynamical systems. The power of the theory
is illustrated by applying it to the Duffing oscillator.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster/,
http://www.physik.fu-berlin.de/~kleinert/ and
http://www.informatik.uni-stuttgart.de/ipvr/bv/personen/schanz.htm

### Spiral Multi-component Structure in Pade - Approximant QCD

We present a graphical method of analyzing the infra-red fixed point
structure of Pade approximant QCD. The analysis shows a spiral multi-component
couplant structure as well as an infra-red attractor behavior of PQCD couplant
for all flavors $0 \le N_{f} \le 16$.Comment: 78 pages, 4 tables, 44 graph

### On an asymptotic estimate of the $n$-loop correction in perturbative QCD

A recently proposed method of estimating the asymptotic behaviour of QCD
perturbation theory coefficients is critically reviewed and shown to contain
numerous invalid mathematical operations and unsubstantiated assumptions. We
discuss in detail why this procedure, based solely on renormalization group
(RG) considerations and analyticity constraints, cannot lead to such estimates.
We stress the importance of correct renormalization scheme (RS) dependence of
any meaningful asymptotic estimate and argue that the unambiguous summation of
QCD perturbation expansions for physical quantities requires information from
outside of perturbation theory itself.Comment: PRA-HEP-92/17, Latex, 20 pages of text plus 5 figures contained in 5
separate PS files. Four of them (corresponding to Figs.1,2,3,5) are appended
at the end of this file, the (somewhat larger one) corresponding to Fig.4 can
be obtained from any of the mentioned E-mail addresses upon request. E-mail
connections: J. Chyla - [email protected]) or h1kchy@dhhdesy3 P. Kolar -
[email protected]

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