102 research outputs found
An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples
This paper builds on our earlier proposal for construction of a positive
inner product for pseudo-Hermitian Hamiltonians and we give several examples to
clarify our method. We show through the example of the harmonic oscillator how
our construction applies equally well to Hermitian Hamiltonians which form a
subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian
matrix Hamiltonians we construct the positive inner product (in the case of
matrices for both real as well as complex eigenvalues). When the
quantum mechanical system cannot be diagonalized exactly, our construction can
be carried out perturbatively and we develop the general formalism for such a
perturbative calculation systematically (for real eigenvalues). We illustrate
how this general formalism works out in practice by calculating the inner
product for a couple of symmetric quantum mechanical theories.Comment: 9 pages, revte
Invisible Higgs boson, continuous mass fields and unHiggs mechanism
We explore the consequences of an electroweak symmetry breaking sector which
exhibits approximately scale invariant dynamics -- i.e., nontrivial fixed point
behavior, as in unparticle models. One can think of an unHiggs as a composite
Higgs boson with a continuous mass distribution. We find it convenient to
represent the unHiggs in terms of a Kallen-Lehmann spectral function, from
which it is simple to verify the generation of gauge boson and fermion masses,
and unitarization of WW scattering. We show that a spectral function with broad
support, which corresponds to approximate fixed point behavior over an extended
range of energy, can lead to an effectively invisible Higgs particle, whose
decays at LEP or LHC could be obscured by background.Comment: 8 page
Lamb Shift in Muonic Hydrogen
The Lamb shift in muonic hydrogen continues to be a subject of experimental
and theoretical investigation. Here my older work on the subject is updated to
provide a complementary calculation of the energies of the 2p-2s transitions in
muonic hydrogen.Comment: 15 pages, no figures. 2 small misprints corrected. Published in Phys.
Rev.
Supersymmetric Corrections to the Threshold Production of Top Quark Pairs
In this paper we investigate supersymmetric effects to the threshold
production cross section of top quark pairs in electron positron annihilation.
In particular, we consider the complete one-loop corrections from the strong
and weak sector of the Minimal Supersymmetric Standard Model.Comment: 18 pages, 7 figure
Amplitude Zeroes in Collinear Processes or What Is Left from a Factorizable 2d Model in Higher Dimensions
We show that for collinear processes, i.e. processes where the incoming and
outgoing momenta are aligned along the same line, the S-matrix of the tree
level 2+1 dimensional Thirring model factorizes: any S - matrix element is a
product of elements. In particular this means nullification of
all collinear amplitudes for .Comment: latex , 8 pp., 2 fig. not include
Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions
We demonstrate how one can construct renormalizable perturbative expansion in
formally nonrenormalizable higher dimensional field theories. It is based on
-expansion and results in a logarithmically divergent perturbation
theory in arbitrary high space-time dimension. First, we consider a simple
example of -component scalar filed theory and then extend this approach to
Abelian and non-Abelian gauge theories with fermions. In the latter case,
due to self-interaction of non-Abelian fields the proposed recipe requires some
modification which, however, does not change the main results. The resulting
effective coupling is dimensionless and is running in accordance with the usual
RG equations. The corresponding beta function is calculated in the leading
order and is nonpolynomial in effective coupling. It exhibits either UV
asymptotically free or IR free behaviour depending on the dimension of
space-time. The original dimensionful coupling plays a role of a mass and is
also logarithmically renormalized. We analyze also the analytical properties of
a resulting theory and demonstrate that in general it acquires several ghost
states with negative and/or complex masses. In the former case, the ghost state
can be removed by a proper choice of the coupling. As for the states with
complex conjugated masses, their contribution to physical amplitudes cancels so
that the theory appears to be unitary.Comment: 32 pages, 20 figure
Lamb shift in muonic deuterium atom
We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic
deuterium (mu d) atom using the three-dimensional quasipotential method in
quantum electrodynamics. The vacuum polarization, nuclear structure and recoil
effects are calculated with the account of contributions of orders alpha^3,
alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed
calculations. The obtained numerical value of the Lamb shift 202.4139 meV can
be considered as a reliable estimate for the comparison with forthcoming
experimental data.Comment: 24 pages, 11 figures. arXiv admin note: text overlap with
arXiv:hep-ph/061229
A geometrical angle on Feynman integrals
A direct link between a one-loop N-point Feynman diagram and a geometrical
representation based on the N-dimensional simplex is established by relating
the Feynman parametric representations to the integrals over contents of
(N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In
particular, the four-point function in four dimensions is proportional to the
volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can
be calculated by splitting into birectangular ones. It is also shown that the
known formula of reduction of the N-point function in (N-1) dimensions
corresponds to splitting the related N-dimensional simplex into N rectangular
ones.Comment: 47 pages, including 42 pages of the text (in plain Latex) and 5 pages
with the figures (in a separate Latex file, requires axodraw.sty) a note and
three references added, minor problem with notation fixe
Observations on the radiative corrections to pion beta-decay
We find that, in the local V-A theory, the radiative corrections to pion
beta-decay involving the weak vector current, when evaluated in the current
algebra (CA) formulation in which quarks are the fundamental underlying fields,
show a small difference with the more elementary calculations based directly on
the pion fields. We show that this difference arises from a specific
short-distance effect that depends on the algebra satisfied by the weak and
electromagnetic currents. On the other hand, we present a simple theoretical
argument that concludes that this difference does not occur when the CA
formulation is compared with the chiral perturbation theory (chiPT) approach.
Comparisons with previous studies, and with a more recent calculation based on
chiPT, are included. We also briefly review the important differences between
the results in the local V-A theory and the Standard Model.Comment: 5 pages, 1 figure. V2: two paragraphs have been added in Section III.
Final version on PR
Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
In the framework of perturbative algebraic quantum field theory a local
construction of interacting fields in terms of retarded products is performed,
based on earlier work of Steinmann. In our formalism the entries of the
retarded products are local functionals of the off shell classical fields, and
we prove that the interacting fields depend only on the action and not on terms
in the Lagrangian which are total derivatives, thus providing a proof of
Stora's 'Action Ward Identity'. The theory depends on free parameters which
flow under the renormalization group. This flow can be derived in our local
framework independently of the infrared behavior, as was first established by
Hollands and Wald. We explicitly compute non-trivial examples for the
renormalization of the interaction and the field.Comment: 76 pages, to appear in Rev. Math. Phy
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