No confinement without Coulomb confinement

We compare the physical potential $V_D(R)$ of an external quark-antiquark pair in the representation $D$ of SU(N), to the color-Coulomb potential $V_{\rm coul}(R)$ which is the instantaneous part of the 44-component of the gluon propagator in Coulomb gauge, D_{44}(\vx,t) = V_{\rm coul}(|\vx|) \delta(t) + (non-instantaneous). We show that if $V_D(R)$ is confining, $\lim_{R \to \infty}V_D(R) = + \infty$, then the inequality $V_D(R) \leq - C_D V_{\rm coul}(R)$ holds asymptotically at large $R$, where $C_D > 0$ is the Casimir in the representation $D$. This implies that $- V_{\rm coul}(R)$ is also confining.Comment: 9 page

Twisted N=8, D=2 super Yang-Mills theory as example of a Hodge-type cohomological theory

It is shown that the dimensional reduction of the N_T=2, D=3 Blau-Thompson model to D=2, i.e., the novel topological twist of N=8, D=2 super Yang-Mills theory, provides an example of a Hodge-type cohomological theory. In that theory the generators of the topological shift, co-shift and gauge symmetry, together with a discrete duality operation, are completely analogous to the de Rham cohomology operators and the Hodge *-operation.Comment: 8 pages, Late

Duality and Superconvergence Relation in Supersymmetric Gauge Theories

We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.Comment: 20 pages, LaTe

Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six ($4 + 2)$-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables.Comment: LaTeX file, 23 page

A new look at the problem of gauge invariance in quantum field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.Comment: Accepted by Physica Scripta. 27 page

Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the $\star$-product among the fields, compatible with the twisted Poincar\'e symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($\theta_{0i}=0$), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.Comment: 16 pages, version to appear in J. Math. Phy

Infra-Red Asymptotic Dynamics of Gauge Invariant Charged Fields: QED versus QCD

The freedom one has in constructing locally gauge invariant charged fields in gauge theories is analyzed in full detail and exploited to construct, in QED, an electron field whose two-point function W(p), up to the fourth order in the coupling constant, is normalized with on-shell normalization conditions and is, nonetheless, infra-red finite; as a consequence the radiative corrections vanish on the mass shell $p^2=\mu^2$ and the free field singularity is dominant, although, in contrast to quantum field theories with mass gap, the eigenvalue $\mu^2$ of the mass operator is not isolated. The same construction, carried out for the quark in QCD, is not sufficient for cancellation of infra-red divergences to take place in the fourth order. The latter divergences, however, satisfy a simple factorization equation. We speculate on the scenario that could be drawn about infra-red asymptotic dynamics of QCD, should this factorization equation be true in any order of perturbation theory.Comment: 30 pages, RevTex, 8 figures included using graphic

Path Integral Quantization of Generalized Quantum Electrodynamics

In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximation of all Green's functions and a discussion about the obtained results are presented.Comment: 25 pages, 5 figure