Hidden variables with nonlocal time

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |psi|^2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory.Comment: 16 pages, accepted for publication in Found. Phys., misprints corrected, references update

Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

Stuckelberg Axions and the Effective Action of Anomalous Abelian Models 1. A unitarity analysis of the Higgs-axion mixing

We analyze the quantum consistency of anomalous abelian models and of their effective field theories, rendered anomaly-free by a Wess-Zumino term, in the case of multiple abelian symmetries. These models involve the combined Higgs-Stuckelberg mechanism and predict a pseudoscalar axion-like field that mixes with the goldstones of the ordinary Higgs sector. We focus our study on the issue of unitarity of these models both before and after spontaneous symmetry breaking and detail the set of Ward identities and the organization of the loop expansion in the effective theory. The analysis is performed on simple models where we show, in general, the emergence of new effective vertices determined by certain anomalous interactions.Comment: 67 pages, 26 figures, replaced with revised final version, to appear on JHE

Non-adiabatic level crossing in (non-) resonant neutrino oscillations

We study neutrino oscillations and the level-crossing probability P_{LZ}=\exp(-\gamma_n\F_n\pi/2) in power-law like potential profiles $A(r)\propto r^n$. After showing that the resonance point coincides only for a linear profile with the point of maximal violation of adiabaticity, we point out that the ``adiabaticity'' parameter $\gamma_n$ can be calculated at an arbitrary point if the correction function \F_n is rescaled appropriately. We present a new representation for the level-crossing probability, P_{LZ}=\exp(-\kappa_n\G_n), which allows a simple numerical evaluation of $P_{LZ}$ in both the resonant and non-resonant cases and where \G_n contains the full dependence of $P_{LZ}$ on the mixing angle $\theta$. As an application we consider the case $n=-3$ important for oscillations of supernova neutrinos.Comment: 4 pages, revtex, 3 eps figure

Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.Comment: 34 page

Boson-fermion unification, superstrings, and Bohmian mechanics

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.Comment: 30 pages, 1 figure, revised, to appear in Found. Phy

Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs

We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p^2=0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the theory is unitary. The proof of unitarity is given both in a form that allows a direct transcription in terms of Feynman amplitudes (cutting rules) and in the operatorial form. The same arguments and conclusions apply verbatim to the case of non-abelian gauge theories where the mass of the vector meson is generated via Higgs mechanism. To the best of our knowledge, there is no mention in the literature on the necessary condition implied by physical unitarity.Comment: References added. 22 pages. Final version to appear in the journa

Couplings of N=1 chiral spinor multiplets

We derive the action for chiral spinor multiplets coupled to vector and scalar multiplets. We give the component form of the action, which contains gauge invariant mass terms for the antisymmetric tensors in the spinor superfield and additional Green-Schwarz couplings to vector fields. We observe that supersymmetry provides mass terms for the scalars in the spinor multiplet which do not arise from eliminating an auxiliary field. We construct the dual action by explicitly performing the duality transformations in superspace and give its component form.Comment: 17 pages, v2 small change

Feedback Effect on Landau-Zener-Stueckelberg Transitions in Magnetic Systems

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intra-molecular couplings.Comment: 4 pages, 3 Postscript figures; paper reorganized, conclusions modifie