22,474 research outputs found
Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
We present the Mathematica application DoFun which allows to derive
Dyson-Schwinger equations and renormalization group flow equations for n-point
functions in a simple manner. DoFun offers several tools which considerably
simplify the derivation of these equations from a given physical action. We
discuss the application of DoFun by means of two different types of quantum
field theories, namely a bosonic O(N) theory and the Gross-Neveu model.Comment: 40 pages, 12 figs.; corresponds to published versio
Bound state equation in the Wilson loop approach with minimal surfaces
The large-distance dynamics in quarkonium systems is investigated, in the
large N limit, through the saturation of Wilson loop averages by minimal
surfaces. Using a representation for the quark propagator in the presence of
the external gluon field based on the use of path-ordered phase factors, a
covariant three-dimensional bound state equation of the Breit-Salpeter type is
derived, in which the interaction potentials are provided by the
energy-momentum vector of the straight segment joining the quark to the
antiquark and carrying a constant linear energy density, equal to the string
tension. The interaction potentials are confining and reduce to the linear
vector potential in the static case and receive, for moving quarks,
contributions from the moments of inertia of the straight segment. The
self-energy parts of the quark propagators induce spontaneous breakdown of
chiral symmetry with a mechanism identical to that of the exchange of one
Coulomb-gluon. The nonrelativistic and ultrarelativistic properties of the
bound state spectrum are studied.Comment: 57 pages, 7 figure
Koopman-von Neumann Formulation of Classical Yang-Mills Theories: I
In this paper we present the Koopman-von Neumann (KvN) formulation of
classical non-Abelian gauge field theories. In particular we shall explore the
functional (or classical path integral) counterpart of the KvN method. In the
quantum path integral quantization of Yang-Mills theories concepts like
gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We
will prove that these same objects are needed also in this classical path
integral formulation for Yang-Mills theories. We shall also explore the
classical path integral counterpart of the BFV formalism and build all the
associated universal and gauge charges. These last are quite different from the
analog quantum ones and we shall show the relation between the two. This paper
lays the foundation of this formalism which, due to the many auxiliary fields
present, is rather heavy. Applications to specific topics outlined in the paper
will appear in later publications.Comment: 46 pages, Late
Coadjoint Orbits, Spin and Dequantization
In this Letter we propose two path integral approaches to describe the
classical mechanics of spinning particles. We show how these formulations can
be derived from the associated quantum ones via a sort of geometrical
dequantization procedure proposed in a previous paper.Comment: 13 pages, Latex, title change
Variational principle for the Wheeler-Feynman electrodynamics
We adapt the formally-defined Fokker action into a variational principle for
the electromagnetic two-body problem. We introduce properly defined boundary
conditions to construct a Poincare-invariant-action-functional of a finite
orbital segment into the reals. The boundary conditions for the variational
principle are an endpoint along each trajectory plus the respective segment of
trajectory for the other particle inside the lightcone of each endpoint. We
show that the conditions for an extremum of our functional are the
mixed-type-neutral-equations with implicit state-dependent-delay of the
electromagnetic-two-body problem. We put the functional on a natural Banach
space and show that the functional is Frechet-differentiable. We develop a
method to calculate the second variation for C2 orbital perturbations in
general and in particular about circular orbits of large enough radii. We prove
that our functional has a local minimum at circular orbits of large enough
radii, at variance with the limiting Kepler action that has a minimum at
circular orbits of arbitrary radii. Our results suggest a bifurcation at some
radius below which the circular orbits become saddle-point extrema. We give a
precise definition for the distributional-like integrals of the Fokker action
and discuss a generalization to a Sobolev space of trajectories where the
equations of motion are satisfied almost everywhere. Last, we discuss the
existence of solutions for the state-dependent delay equations with slightly
perturbated arcs of circle as the boundary conditions and the possibility of
nontrivial solenoidal orbits
Modified Partition Functions, Consistent Anomalies and Consistent Schwinger Terms
A gauge invariant partition function is defined for gauge theories which
leads to the standard quantization. It is shown that the descent equations and
consequently the consistent anomalies and Schwinger terms can be extracted from
this modified partition function naturally.Comment: 25 page
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