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F. Kleefeld

Publications and source records attributed to F. Kleefeld.

At least 19 recordsLinked to original sources
arXiv2012

Complex Covariance

According to some generalized correspondence principle the classical limit of a non-Hermitian Quantum theory describing quantum degrees of freedom is expected to be well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity has been developed by Einstein merely for real-valued space-time and four-momentum we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, yet also to the non-Hermitian Klein-Gordon and Dirac equations which are to lay the foundations of a non-Hermitian quantum theory.

math-ph↗
arXiv2009

The construction of a general inner product in non-Hermitian quantum theory and some explanation for the nonuniqueness of the C operator in PT quantum mechanics

Most recently it has been observed e.g. by Bender and Klevansky (arXiv:0905.4673 [hep-th]) that the C-operator related to a PT-symmetric non-Hermitian Hamilton operator is not unique. Moreover it has been remarked by Shi and Sun (arXiv:0905.1771 [hep-th]) very recently that there seems to exist a well defined inner product in the context of the Hamilton operator of the PT-symmetric non-Hermitian Lee model yielding a different C-operator as compared to the one previously derived by Bender et al.. The puzzling observations of both manuscripts are reconciled and explained in the present manuscript as follows: the actual form of the metric operator (and the induced C-operator) related to some non-Hermitian Hamilton operator constructed along the lines of Shi and Su depends on the chosen normalization of the left and right eigenvectors of the Hamilton operator under consideration and is therefore ambiguous. For a specific PT-symmetric 2x2-matrix Hamilton operator it is shown that - by a suitable choice of the norm of its eigenvectors - the metric operator yielding a positive semi-definite inner product can be made even independent of the parameters of the considered Hamilton operator. This surprising feature makes in turn the obtained metric operator rather unique and attractive. For later convenience the metric operator for the Bosonic and Fermionic (anti)causal harmonic oscillator is derived.

hep-th↗
arXiv2008

On how to complete the Dynamical Generation of Quark-Level Linear Sigma Model like Theories beyond one Loop

A self-consistent strategy is proposed to complete in a renormalization scheme independent way the dynamical generation of Quark-Level Linear Sigma Model like Lagrangean theories beyond one loop like the theories of strong and electroweak interactions. The present discussion refers for simplicity to scalar and pseudoscalar degrees of freedom only while disregarding yet - without loss of generality - vector and axial vector degrees of freedom. Moreover points the discussion to approximations underlying dimensional and implicit regularization as presently used.

hep-ph↗
arXiv2007

Constituent and current quark masses at low chiral energies

Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the Quark-Level Linear $σ$ Model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses which reproduce the experimental pion and kaon masses very accurately, by simple additivity. Moreover, the masses of the light scalar mesons $σ(600)$ and $κ(800)$ can be obtained straightforwardly from the constituent quark masses. In contrast, the usual nonstrange and strange current quark masses employed by Chiral Perturbation Theory do not allow a simple quantitative explanation of the pion and kaon masses.

hep-ph↗
arXiv2007

On the absence and presence of pole(s) in fermion propagator in the simple model with mass generation

Within the Pauli-Villars regularization technique the fermion propagator is studied in the framework of Schwinger-Dyson equations in the Euclidean space. Making the generalization of Fukuda and Kugo proposals, the analytical continuation is performed into the timelike region of fourmomenta. The massive gauge boson kernel is considered and the fermion propagator pole structure is discussed in detail.

hep-ph↗
arXiv2007

Comment on "Mass and Width of the Lowest Resonance in QCD"

I. Caprini's, G. Colangelo's, and H. Leutwyler's (CCL) article "Mass and Width of the Lowest Resonance in QCD", Phys. Rev. Lett. 96, 132001 (2006) [hep-ph/0512364], is critically reviewed. The present comment is devoted to complement a recent experimental discussion (D.V. Bugg, J. Phys. G 34, 151 (2007) [hep-ph/0608081]) of short-comings in the CCL analysis, by presenting theoretical arguments pointing at a serious flaw in the theoretical formalism used by CCL, and also at the unlikeliness of their tiny error bars in the sigma-meson mass and width. The criticism made in the comment applies analogously to the analysis on the kappa-meson mass performed in the article "The K0*(800) scalar resonance from Roy-Steiner representations of pi K scattering" published as S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C 48, 553 (2006) [hep-ph/0607133].

hep-ph↗
arXiv2006

The nature of $σ$, $κ$, $a_0(980)$ and $f_0(980)$

Masses and widths of the four light scalar mesons $σ$, $κ$, $a_0$(980) and $f_0$(980) may be reproduced in a model where mesons scatter via a $q\bar{q}$ loop. A transition potential is used to couple mesons to $q\bar{q}$ at a radius of $\sim 0.57$ fm. Inside this radius, there is an infinite bare spectrum of confined $q\bar{q}$ states, for which a harmonic oscillator is chosen here. The coupled-channel system approximately reproduces the features of both light and heavy meson spectroscopy. The generation of $σ$, $κ$, $a_0(980)$ and $f_0(980)$ is a balance between attraction due to the $q\bar q$ loop and suppression of the amplitudes at the Adler zeros. Phase shifts increase more rapidly as the coupling constant to the mesons increases. This leads to resonant widths which decrease with increasing coupling constant - a characteristically non-perturbative effect.

hep-ph↗
arXiv2006

On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm

A simple derivation of a meaningful, manifestly covariant inner product for real Klein-Gordon (KG) fields with positive semi-definite norm is provided which turns out - assuming a symmetric bilinear form - to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric Quantum Mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.

quant-ph↗
arXiv2006

Coulomb-scattering and eta - eta-prime mixing angle

The fascinating physics underlying eta and eta-prime mesons can be studied theoretically and experimentally in various contexts. In this presentation we want to turn our attention to two important uncorrelated aspects of this vivid research field which provide yet unexpected challenges or surprises. First we discuss open questions in the theoretical treatment of Coulomb-interaction in the context of reaction processes like p p --> p p eta. Then we review eta - eta-prime and sigma(600) - f_0(980) mixing in the U(3) x U(3) Linear Sigma Model and extract information on eta - eta-prime mixing and the K*0(800) resonance from meson-meson scattering.

nucl-th↗
arXiv2005

On a new unitarization scheme inspired by Dalitz and Tuan applied to meson-meson and meson-baryon scattering

A new crossing symmetric unitarization scheme conveniently applied to meson-meson and meson-baryon scattering amplitudes is shortly proposed which can be not only used by theoreticians to unitarize arbitrary theoretical reaction amplitudes resulting from phenomenological Lagrangeans for mesons and baryons, yet also by experimentalists to generate realistic unitary fitting formulae for meson-meson and meson-baryon scattering observables sharing on one hand all the features of the underlying theoretical amplitudes, on the other hand allowing direct comparison to these amplitudes. The new unitarization scheme has been inspired by the Dalitz and Tuan representation, the basic ansatz of which is that "... the phases caused by different sources add ..." (using the words of B.S. Zou, D.V. Bugg, Phys. Rev. D 50 (1994) 591).

hep-ph↗
arXiv2005

Kurt Symanzik - a stable fixed point beyond triviality

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.

hep-th↗
arXiv2005

On (non-Hermitian) Lagrangeans in (particle) physics and their dynamical generation

On the basis of a new method to derive the effective action the nonperturbative concept of "dynamical generation" is explained. A non-trivial, non-Hermitian and PT-symmetric solution for Wightman's scalar field theory in four dimensions is dynamically generated, rehabilitating Symanzik's precarious phi**4-theory with a negative quartic coupling constant as a candidate for an asymptotically free theory of strong interactions. Finally it is shown making use of dynamically generation that a Symanzik-like field theory with scalar confinement for the theory of strong interactions can be even suggested by experiment.

hep-th↗
arXiv2004

Non-Hermitian Quantum Theory and its Holomorphic Representation: Introduction and Applications

This article contains a short summary of an oral presentation in the 2nd International Workshop on "Pseudo-Hermitian Hamiltonians in Quantum Physics" (14.-16.6.2004, Villa Lanna, Prague, Czech Republic). The purpose of the presentation has been to introduce a non-Hermitian generalization of pseudo-Hermitian Quantum Theory allowing to reconcile the orthogonal concepts of causality, Poincare invariance, analyticity, and locality. We conclude by considering interesting applications like non-Hermitian supersymmetry.

hep-th↗
arXiv2004

Non-Hermitian Quantum Theory and its Holomorphic Representation: Introduction and Some Applications

Present Hermitian Quantum Theory, i.e. Quantum Mechanics and Quantum Field Theory, is revised and replaced by a consistent non-Hermitian formalism called non-Hermitian Quantum Theory (NHQT) or (Anti)Causal Quantum Theory ((A)CQT) after lining out some inherent inconsistencies and problems arising in the context of causality, which is observed to introduce an indefinite metric in canonical commutation relations. Choosing some (very selective) historical approach to introduce necessary terminology and explain complications when quantizing non-Hermitian systems in the presence of an indefinite metric we propose a way how to construct a causal, analytic, Poincare invariant, and local NHQT, the spacial representation of which is related to the so-called holomorphic representation used in complex analysis. Besides providing a revised antiparticle, spinor, and probability concept, a new neutrino Lagrangean, two distinct time-reversal operations, and generalized non-Hermitian Poincare transformations, we will apply NHQT to consider three important issues: PT-symmetry and non-Hermitian similarity transforms, non-Hermitian supersymmetry, and the construction of an asymptotically free theory of strong interactions without gluons.

hep-th↗
arXiv2003

Is a quantum theory of resonances really time asymmetric?

The title "Time Asymmetric Quantum Theory: the Theory of Resonances" (without questionmark) of the CFIF workshop (23.-26.7.2003, Lisbon, Portugal) implies that the theoretical description of resonances is uniquely described by the formalism of A. Bohm et al. reflecting the title of the workshop. Our presentation in this workshop tries to introduce an apparently inequivalent, alternative feasible relativistic formalism provided by the author under the name "(Anti)Causal Quantum Theory" which is compared to the former.

hep-th↗
arXiv2003

The Light and Heavy Scalars in Unitarized Coupled Channel and Lagrangian Approaches

Using ideas underlying the flavour-blind "Nijmegen Unitarised Meson Model" we try to understand on the basis of a system of Schroedinger equations with one meson-meson and one (spinless) quark-antiquark channel coupled by a simple delta-shell transition potential the formation of (e.g. scalar) meson-meson scattering singularities in the complex momentum and energy plane. Surprisingly we are able to describe without direct meson-meson interaction and without any need for glueballs the whole known scalar meson spectrum. "Light" scalar mesons (e.g. f0(600), kappa(800), f0(980), a0(985), D*0(2290), ...) are identified to belong to the spectrum of the transition potential, while "heavy" scalars (e.g. f0(1370), K*0(1430), f0(1500), f0(1710), a0(1450), D*0(2621) (?), D*0(2825) (?), D*sJ(2928) (?), ...) are related to the confinement spectrum. Due to the particular value of the charm-strange reduced quark mass level-(anti)crossing in the complex momentum plane occurs which relates the BABAR state Ds(2317) to the bare groundstate of the confinement spectrum, while the respective groundstate of the transition potential ends up as D*sJ(2782) (?). We conclude with a short comment on (our) recent progress in the consistent quantum field theoretical effective description of resonances within a Lagrangian framework.

hep-ph↗