10,479 research outputs found
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
Inversion, Iteration, and the Art of Dual Wielding
The humble ("dagger") is used to denote two different operations in
category theory: Taking the adjoint of a morphism (in dagger categories) and
finding the least fixed point of a functional (in categories enriched in
domains). While these two operations are usually considered separately from one
another, the emergence of reversible notions of computation shows the need to
consider how the two ought to interact. In the present paper, we wield both of
these daggers at once and consider dagger categories enriched in domains. We
develop a notion of a monotone dagger structure as a dagger structure that is
well behaved with respect to the enrichment, and show that such a structure
leads to pleasant inversion properties of the fixed points that arise as a
result. Notably, such a structure guarantees the existence of fixed point
adjoints, which we show are intimately related to the conjugates arising from a
canonical involutive monoidal structure in the enrichment. Finally, we relate
the results to applications in the design and semantics of reversible
programming languages.Comment: Accepted for RC 201
- …