213 research outputs found
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
On the notion of potential in quantum gravity
The problem of consistent definition of the quantum corrected gravitational
field is considered in the framework of the -matrix method. Gauge dependence
of the one-particle-reducible part of the two-scalar-particle scattering
amplitude, with the help of which the potential is usually defined, is
investigated at the one-loop approximation. The -terms in the potential,
which are of zero order in the Planck constant are shown to be
independent of the gauge parameter weighting the gauge condition in the action.
However, the -terms, proportional to describing the first
proper quantum correction, are proved to be gauge-dependent. With the help of
the Slavnov identities, their dependence on the weighting parameter is
calculated explicitly. The reason the gauge dependence originates from is
briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure
Explicit construction of the classical BRST charge for nonlinear algebras
We give an explicit formula for the Becchi-Rouet-Stora-Tyutin (BRST) charge
associated with Poisson superalgebras. To this end, we split the master
equation for the BRST charge into a pair of equations such that one of them is
equivalent to the original one. We find the general solution to this equation.
The solution possesses a graphical representation in terms of diagrams.Comment: 9 pages; v2,v3 minor corrections, references added for v
Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory
We demonstrate the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory
that is described by the coupled Lagrangian densities (which incorporate the
celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-)
BRST symmetry transformations is ensured by the existence of a Curci-Ferrari
type restriction that emerges from the superfield formalism as well as from the
equations of motion that are derived from the above coupled Lagrangian
densities. We show the invariance of the action from the point of view of the
symmetry considerations as well as superfield formulation. We discuss,
furthermore, the topological term within the framework of superfield formalism
and provide the geometrical meaning of its invariance under the (anti-) BRST
symmetry transformations.Comment: LaTeX file, 22 pages, journal versio
Free Abelian 2-Form Gauge Theory: BRST Approach
We discuss various symmetry properties of the Lagrangian density of a four (3
+ 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge
theory is endowed with a Curci-Ferrari type condition which happens to be a key
signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the
above condition that the nilpotent BRST and anti-BRST symmetries of the theory
are found to be absolutely anticommuting in nature. For our present 2-form
gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry
properties of the Lagrangian densities and derive the corresponding conserved
charges. The algebraic structure, obeyed by the above conserved charges, is
deduced and the constraint analysis is performed with the help of the
physicality criteria where the conserved and nilpotent (anti-)BRST charges play
completely independent roles. These physicality conditions lead to the
derivation of the above Curci-Ferrari type restriction, within the framework of
BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc
Gauge dependence of effective gravitational field
The problem of gauge independent definition of effective gravitational field
is considered from the point of view of the process of measurement. Under
assumption that dynamics of the measuring apparatus can be described by the
ordinary classical action, effective Slavnov identities for the generating
functionals of Green functions corresponding to a system of arbitrary
gravitational field measured by means of scalar particles are obtained. With
the help of these identities, the total gauge dependence of the non-local part
of the one-loop effective apparatus action, describing the long-range quantum
corrections, is calculated. The value of effective gravitational field inferred
from the effective apparatus action is found to be gauge-dependent. A probable
explanation of this result, referring to a peculiarity of the gravitational
interaction, is given.Comment: Revised version as publishe
WT identities for proper vertices and renormalization in a superspace formulation of gauge theories
We formulate the WT identity for proper vertices in a simple and compact form
in a superspace formulation of gauge
theories proposed earlier. We show this WT identity (together with a subsidiary
constraint) lead, in transparent way, the superfield superspace multiplet
renormalizations formulated earlier (and shown to explain symmetries of
Yang-Mills theory renormalization).Comment: 18 pages, Latex , Revised version, Appeared in PRD 5
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