A study of the violation of the Bell-CHSH inequality

The violation of the Bell-CHSH inequality for bipartite systems is discussed by making use of the pseudospin operators which enable us to group all modes of the Hilbert space of the system in pairs. We point out that a single pair can be already employed to perform a test of the Bell-CHSH inequality in order to check out its violation. The mechanism is illustrated with the help of $N00N$ states as well as with coherent and squeezed states.Comment: 8 pages, expanded versio

Shadow Fields and Local Supersymmetric Gauges

To control supersymmetry and gauge invariance in super-Yang-Mills theories we introduce new fields, called shadow fields, which enable us to enlarge the conventional Faddeev-Popov framework and write down a set of useful Slavnov-Taylor identities. These identities allow us to address and answer the issue of the supersymmetric Yang-Mills anomalies, and to perform the conventional renormalization programme in a fully regularization-independent way.Comment: 2

Entanglement and maximal violation of the CHSH inequality in a system of two spins j: a novel construction and further observations

We study the CHSH inequality for a system of two spin $j$ particles, for generic $j$. The CHSH operator is constructed using a set of unitary, Hermitian operators $\left\{ A_{1},A_{2},B_{1},B_{2}\right\}$. The expectation value of the CHSH operator is analyzed for the singlet state $\left|\psi_{s}\right\rangle$. Being $\left|\psi_{s}\right\rangle$ an entangled state, a violation of the CHSH inequality compatible with Tsirelson's bound is found. Although the construction employed here differs from that of [1], full agreement is recovered.Comment: 6 page

The Gribov horizon and spontaneous BRST symmetry breaking

An equivalent formulation of the Gribov-Zwanziger theory accounting for the gauge fixing ambiguity in the Landau gauge is presented. The resulting action is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact BRST invariance which is spontaneously broken due to the presence of the Gribov horizon. This spontaneous symmetry breaking can be described in a purely algebraic way through the introduction of a pair of auxiliary fields which give rise to a set of linearly broken Ward identities. The Goldstone sector turns out to be decoupled. The underlying exact nilpotent BRST invariance allows to employ BRST cohomology tools within the Gribov horizon to identify renormalizable extensions of gauge invariant operators. Using a simple toy model and appropriate Dirac bracket quantization, we discuss the time-evolution invariance of the operator cohomology. We further comment on the unitarity issue in a confining theory, and stress that BRST cohomology alone is not sufficient to ensure unitarity, a fact, although well known, frequently ignored.Comment: 13 pages. v2: corrected typ

Mermin's inequalities in Quantum Field Theory

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum $\vert 0 \rangle$, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.Comment: 8 pages, minor changes, results unchange

Renormalization and finiteness of topological BF theories

We show that the BF theory in any space-time dimension, when quantized in a certain linear covariant gauge, possesses a vector supersymmetry. The generator of the latter together with those of the BRS transformations and of the translations form the basis of a superalgebra of the Wess-Zumino type. We give a general classification of all possible anomalies and invariant counterterms. Their absence, which amounts to ultraviolet finiteness, follows from purely algebraic arguments in the lower-dimensional cases.Comment: 27 p., Latex fil

Adler-Bardeen theorem and vanishing of the gauge beta function

The proof of the non-renormalization theorem for the gauge anomaly of four-dimensional theories is extended to the case of models with a vanishing one-loop gauge beta function