1,250 research outputs found
SU(m|n) supersymmetric Calogero-Sutherland model confined in harmonic potential
In this work, we study a continuous quantum system of a mixture of bosons and
fermions with the supersymmetry SU(m|n). The particles are confined in a
harmonic well and interact with each other through the 1/r2 interaction. The
ground state wavefunction is constructed explicitly for the most general
SU(m|n) case, with the ground state energy given explicitly. The full energy
spectrum of excitations in the SU(m|n) model is also equal spaced. In the
limiting case where there are no bosons in the system, our results reduce to
those obtained previously.Comment: 9 pages, preprint of ETH-Lausanne (August 1996
No radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences
The issue intensively claimed in the literature on the generation of a
CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections
owing to a CPT violating interaction -- the axial coupling of fermions with a
constant vector field b_\m -- is mistaken. The presence of massless gauge
field triggers IR divergences that might show up from the UV subtractions,
therefore, so as to deal with the (actual physical) IR divergences, the
Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL
renormalization method, has to be adopted. The proof on the non generation of
such a Chern-Simons-like term is done, independent of any kind of
regularization scheme, at all orders in perturbation theory.Comment: In honor of Prof. Manfred Schweda (1939-2017). Work presented at the
XXXVIII National Meeting on Particle Physics and Fields, September 18-22,
2017 - Passa Quatro - Minas Gerais - Brazil. Reference [46] correcte
The asymmetry of the dimension 2 gluon condensate: the zero temperature case
We provide an algebraic study of the local composite operators A_\mu
A_\nu-\delta_{\mu\nu}/d A^2 and A^2, with d=4 the spacetime dimension. We prove
that these are separately renormalizable to all orders in the Landau gauge.
This corresponds to a renormalizable decomposition of the operator A_\mu A_\nu
into its trace and traceless part. We present explicit results for the relevant
renormalization group functions to three loop order, accompanied with various
tests of these results. We then develop a formalism to determine the zero
temperature effective potential for the corresponding condensates, and recover
the already known result for \neq 0, together with <A_\mu
A_\nu-\delta_{\mu\nu}/d A^2>=0, a nontrivial check that the approach is
consistent with Lorentz symmetry. The formalism is such that it is readily
generalizable to the finite temperature case, which shall allow a future
analytical study of the electric-magnetic symmetry of the condensate,
which received strong evidence from recent lattice simulations by Chernodub and
Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase
diagram.Comment: 25 page
An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3
A rigorous algebraic proof of the full finiteness in all orders of
perturbation theory is given for the Yang-Mills-Chern-Simons theory in a
general three-dimensional Riemannian manifold. We show the validity of a trace
identity, playing the role of a local form of the Callan-Symanzik equation, in
all loop orders, which yields the vanishing of the beta-functions associated to
the topological mass and gauge coupling constant as well as the anomalous
dimensions of the fields.Comment: 5 pages, revte
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