642 research outputs found
Axial anomalies in gauge theory by exact renormalization group method
The global chiral symmetry of a gauge theory is studied in the
framework of renormalization group (RG). The theory is defined by the RG flow
equations in the infrared cutoff \L and the boundary conditions for the
relevant couplings. The physical theory is obtained at \L=0. In our approach
the symmetry is implemented by choosing the boundary conditions for the
relevant couplings not at the ultraviolet point \L=\L_0\to\infty but at the
physical value \L=0. As an illustration, we compute the triangle axial
anomalies.Comment: 11 pages + 1 appended EPS figure, LaTeX, UPRF 94-39
Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory
We discuss the relation between the Gell-Mann-Low beta function and the
``flowing couplings'' of the Wilsonian action S_\L[\phi] of the exact
renormalization group (RG) at the scale \L. This relation involves the
ultraviolet region of \L so that the condition of renormalizability is
equivalent to the Callan-Symanzik equation. As an illustration, by using the
exact RG formulation, we compute the beta function in Yang-Mills theory to one
loop (and to two loops for the scalar case). We also study the infrared (IR)
renormalons. This formulation is particularly suited for this study since: )
\L plays the r\^ole of a IR cutoff in Feynman diagrams and non-perturbative
effects could be generated as soon as \L becomes small; ) by a
systematical resummation of higher order corrections the Wilsonian flowing
couplings enter directly into the Feynman diagrams with a scale given by the
internal loop momenta; ) these couplings tend to the running coupling at
high frequency, they differ at low frequency and remain finite all the way down
to zero frequency.Comment: 19 pages, 6 figures, LaTex, uses epsfig, rotatin
Gauge invariant action at the ultraviolet cutoff
We show that it is possible to formulate a gauge theory starting from a local
action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has
to require that fields in the UV action and the fields in the effective action
are not the same but related by a local field transformation. The few relevant
parameters involved in this transformation (six for the gauge theory),
are perturbatively fixed by the gauge symmetry.Comment: 5 pages, Latex, no figure
BRS "Symmetry", prehistory and history
Prehistory - Starting from 't Hooft's (1971) we have a short look at Taylor's
and Slavnov's works (1971-72) and at the lectures given by Rouet and Stora in
Lausanne-1973 which determine the transition from pre-history to history.
History - We give a brief account of the main analyses and results of the BRS
collaboration concerning the renormalized gauge theories, in particular the
method of the regularization independent, algebraic renormalization, the
algebraic proof of S-matrix unitarity and that of gauge choice independence of
the renormalized physics. We conclude this report with a suggestion to the
crucial question: what could remain of BRS invariance beyond perturbation
theory.Comment: Talk given at: A Special day in honour of Raymond Stora, Annecy, July
8, 201
Lower body design of the âiCubâ a human-baby like crawling robot
The development of robotic cognition and a greater understanding of human cognition form two of the current greatest challenges of science. Within the RobotCub project the goal is the development of an embodied robotic child (iCub) with the physical and ultimately cognitive abilities of a 2frac12 year old human baby. The ultimate goal of this project is to provide the cognition research community with an open human like platform for understanding of cognitive systems through the study of cognitive development. In this paper the design of the mechanisms adopted for lower body and particularly for the leg and the waist are outlined. This is accompanied by discussion on the actuator group realisation in order to meet the torque requirements while achieving the dimensional and weight specifications. Estimated performance measures of the iCub are presented
On a class of embeddings of massive Yang-Mills theory
A power-counting renormalizable model into which massive Yang-Mills theory is
embedded is analyzed. The model is invariant under a nilpotent BRST
differential s. The physical observables of the embedding theory, defined by
the cohomology classes of s in the Faddeev-Popov neutral sector, are given by
local gauge-invariant quantities constructed only from the field strength and
its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the
journa
Constructive algebraic renormalization of the abelian Higgs-Kibble model
We propose an algorithm, based on Algebraic Renormalization, that allows the
restoration of Slavnov-Taylor invariance at every order of perturbation
expansion for an anomaly-free BRS invariant gauge theory. The counterterms are
explicitly constructed in terms of a set of one-particle-irreducible Feynman
amplitudes evaluated at zero momentum (and derivatives of them). The approach
is here discussed in the case of the abelian Higgs-Kibble model, where the zero
momentum limit can be safely performed. The normalization conditions are
imposed by means of the Slavnov-Taylor invariants and are chosen in order to
simplify the calculation of the counterterms. In particular within this model
all counterterms involving BRS external sources (anti-fields) can be put to
zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page
Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance
We study the formulation of the Wilson renormalization group (RG) method for
a non-Abelian gauge theory. We analyze the simple case of and show that
the local gauge symmetry can be implemented by suitable boundary conditions for
the RG flow. Namely we require that the relevant couplings present in the
physical effective action, \ie the coefficients of the field monomials with
dimension not larger than four, are fixed to satisfy the Slavnov-Taylor
identities. The full action obtained from the RG equation should then satisfy
the same identities. This procedure is similar to the one we used in QED. In
this way we avoid the cospicuous fine tuning problem which arises if one gives
instead the couplings of the bare Lagrangian. To show the practical character
of this formulation we deduce the perturbative expansion for the vertex
functions in terms of the physical coupling at the subtraction point
and perform one loop calculations. In particular we analyze to this order some
ST identities and compute the nine bare couplings. We give a schematic proof of
perturbative renormalizability.Comment: 25 pages + 4 figures appended as PostScript file, LaTeX style, UPRF
93-388, explanations adde
BRS symmetry for Yang-Mills theory with exact renormalization group
In the exact renormalization group (RG) flow in the infrared cutoff
one needs boundary conditions. In a previous paper on Yang-Mills theory
we proposed to use the nine physical relevant couplings of the effective action
as boundary conditions at the physical point (these couplings are
defined at some non-vanishing subtraction point ). In this paper we
show perturbatively that it is possible to appropriately fix these couplings in
such a way that the full set of Slavnov-Taylor (ST) identities are satisfied.
Three couplings are given by the vector and ghost wave function normalization
and the three vector coupling at the subtraction point; three of the remaining
six are vanishing (\eg the vector mass) and the others are expressed by
irrelevant vertices evaluated at the subtraction point. We follow the method
used by Becchi to prove ST identities in the RG framework. There the boundary
conditions are given at a non-physical point , so that
one avoids the need of a non-vanishing subtraction point.Comment: 22 pages, LaTeX style, University of Parma preprint UPRF 94-41
Slavnov-Taylor Parameterization for the Quantum Restoration of BRST Symmetries in Anomaly-Free Gauge Theories
It is shown that the problem of the recursive restoration of the
Slavnov-Taylor (ST) identities at the quantum level for anomaly-free gauge
theories is equivalent to the problem of parameterizing the local approximation
to the quantum effective action in terms of ST functionals, associated with the
cohomology classes of the classical linearized ST operator. The ST functionals
of dimension <=4 correspond to the invariant counterterms, those of dimension
>4 generate the non-symmetric counterterms upon projection on the action-like
sector. At orders higher than one in the loop expansion there are additional
contributions to the non-invariant counterterms, arising from known lower order
terms. They can also be parameterized by using the ST functionals. We apply the
method to Yang-Mills theory in the Landau gauge with an explicit mass term
introduced in a BRST-invariant way via a BRST doublet. Despite being
non-unitary, this model provides a good example where the method devised in the
paper can be applied to derive the most general solution for the action-like
part of the quantum effective action, compatible with the fulfillment of the ST
identities and the other relevant symmetries of the model, to all orders in the
loop expansion. The full dependence of the solution on the normalization
conditions is given.Comment: 23 pages. Final version published in the journa
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