Microcanonical Ensemble and Algebra of Conserved Generators for Generalized Quantum Dynamics

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.Comment: Plain TeX, 18 pages. Corrected report number onl

Spectral Function of Fermion Coupled with Massive Vector Boson at Finite Temperature in Gauge Invariant Formalism

We investigate spectral properties of a fermion coupled with a massive gauge boson with a mass m at finite temperature (T) in the perturbation theory. The massive gauge boson is introduced as a U(1) gauge boson in the Stueckelberg formalism with a gauge parameter \alpha. We find that the fermion spectral function has a three-peak structure for T \sim m irrespective of the choice of the gauge parameter, while it tends to have one faint peak at the origin and two peaks corresponding to the normal fermion and anti-plasmino excitations familiar in QED in the hard thermal loop approximation for T \gg m. We show that our formalism successfully describe the fermion spectral function in the whole T region with the correct high-T limit except for the faint peak at the origin, although some care is needed for choice of the gauge parameter for T \gg m. We clarify that for T \sim m, the fermion pole is almost independent of the gauge parameter in the one-loop order, while for T \gg m, the one-loop analysis is valid only for \alpha \ll 1/g where g is the fermion-boson coupling constant, implying that the one-loop analysis can not be valid for large gauge parameters as in the unitary gauge.Comment: 28pages, 11figures. v2: typos fixe

A Chiral Spin Theory in the Framework of an Invariant Evolution Parameter Formalism

We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent quantized formalism dealing with off-shell particles with spin. Our basic requirement is that the second order equation in the theory is of the Schr\"{o}dinger-Stueckelberg type, which exhibits features of both the Klein-Gordon and Schr\"{o}dinger equations. This requirement restricts the structure of the first order equation, in particular, to a chiral form. One thus obtains, in a natural way, a theory of chiral form for massive particles, which may contain both left and right chiralities, or just one of them. We observe that by iterating the first order system, we are able to obtain second order forms containing the transverse and longitudinal momentum relative to a time-like vector $t_{\mu}t^{\mu}=-1$ used to maintain covariance of the theory. This time-like vector coincides with the one used by Horwitz, Piron, and Reuse to obtain an invariant positive definite space-time scalar product, which permits the construction of an induced representation for states of a particle with spin. We discuss the currents and continuity equations, and show that these equations of motion and their currents are closely related to the spin and convection parts of the Gordon decomposition of the Dirac current. The transverse and longitudinal aspects of the particle are complementary, and can be treated in a unified manner using a tensor product Hilbert space. Introducing the electromagnetic field we find an equation which gives rise to the correct gyromagnetic ratio, and is fully Hermitian under the proposed scalar product. Finally, we show that the original structure of Dirac'sComment: Latex, 61 pages. Minor revisions. To be published in J. Math. Phy

Geometrical approach to the proton spin decomposition

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of this approach follows from a mechanism similar to the one used in the famous Stueckelberg trick. Stressing the fact that the Lorentz symmetry does not force the gauge potential to transform as a Lorentz four-vector, we show that the Chen et al. approach is Lorentz covariant provided that one uses the suitable Lorentz transformation law. We also make an attempt to summarize the present situation concerning the proton spin decomposition. We argue that the ongoing debates concern essentially the physical interpretation and are due to the plurality of the adopted pictures. We discuss these different pictures and propose a pragmatic point of view.Comment: 39 pages, 1 figure, updated version to appear in PRD (2013

Non-Trivial Ghosts and Second Class Constraints

In a model in which a vector gauge field $W_\mu^a$ is coupled to an antisymmetric tensor field $\phi_{\mu\nu}^a$ possessing a pseudoscalar mass, it has been shown that all physical degrees of freedom reside in the vector field. Upon quantizing this model using the Faddeev-Popov procedure, explicit calculation of the two-point functions $$and$$ at one-loop order seems to have yielded the puzzling result that the effective action generated by radiative effects has more physical degrees of freedom than the original classical action. In this paper we point out that this is not in fact a real effect, but rather appears to be a consequence of having ignored a "ghost" field arising from the contribution to the measure in the path integral arising from the presence of non-trivial second-class constraints. These ghost fields couple to the fields $W_\mu^a$ and $\phi_{\mu\nu}^a$, which makes them distinct from other models involving ghosts arising from second-class constraints (such as massive Yang-Mills (YM) models) that have been considered, as in these other models such ghosts decouple. As an alternative to dealing with second class constraints, we consider introducing a "Stueckelberg field" to eliminate second-class constraints in favour of first-class constraints and examine if it is possible to then use the Faddeev-Popov quantization procedure. In the Proca model, introduction of the Stueckelberg vector is equivalent to the Batalin-Fradkin-Tyutin (BFT) approach to converting second-class constraints to being first class through the introduction of new variables. However, introduction of a Stueckelberg vector is not equivalent to the BFT approach for the vector-tensor model. In an appendix, the BFT procedure is applied to the pure tensor model and a novel gauge invariance is found.Comment: 23 pages, LaTeX2e forma

Time-Shift in the OPERA set-up: proof against superluminal neutrinos without the need of knowing the CERN-LNGS distance and Reminiscences on the origin of the Gran Sasso Lab, of the 3rd neutrino and of the "Teramo Anomaly"

The LVD time stability allows to establish a time-shift in the OPERA experiment, thus providing the first proof against Superluminal neutrinos, using the horizontal muons of the "Teramo Anomaly". This proof is particularly interesting since does not need the knowledge of the distance between the place where the neutrinos are produced (CERN) and the place where they are detected (LNGS). Since the Superluminal neutrinos generated in the physics community a vivid interest in good and bad behaviour in physics research, the author thought it was appropriate to recall the origin of the Gran Sasso Lab, of the 3rd neutrino, of the horizontal muons due to the "Teramo Anomaly" and of the oscillation between leptonic flavours, when the CERN-Gran Sasso neutrino beam was included in the project for the most powerful underground Laboratory in the world.Comment: 35 pages, 25 Figures, Invited paper at the Gran Sasso mini-Workshop on LNGS results on the neutrino velocity topic, Gran Sasso, Italy, 28 March 201

Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism

We wish to study an application of Stueckelberg's relativistic quantum theory in the framework of general relativity. We study the form of the wave equation of a massive body in the presence of a Schwarzschild gravitational field. We treat the mathematical behavior of the wavefunction also around and beyond the horizon (r=2M). Classically, within the horizon, the time component of the metric becomes spacelike and distance from the origin singularity becomes timelike, suggesting an inevitable propagation of all matter within the horizon to a total collapse at r=0. However, the quantum description of the wave function provides a different understanding of the behavior of matter within the horizon. We find that a test particle can almost never be found at the origin and is more probable to be found at the horizon. Matter outside the horizon has a very small wave length and therefore interference effects can be found only on a very small atomic scale. However, within the horizon, matter becomes totally "tachionic" and is potentially "spread" over all space. Small location uncertainties on the atomic scale become large around the horizon, and different mass components of the wave function can therefore interfere on a stellar scale. This interference phenomenon, where the probability of finding matter decreases as a function of the distance from the horizon, appears as an effective gravitational repulsion.Comment: 20 pages, 6 figure

The Supersymmetric Stueckelberg Mass and Overcoming the Fayet-Iliopoulos Mechanism for Breaking Symmetry

Gauge invariant generation of mass for supersymmetric U(1) vector field through use of a chiral Stueckelberg superfield is considered. When a Fayet-Iliopoulos D term is also present, no breaking of supersymmetry ever occurs so long as the Stueckelberg mass is not zero. A moduli space in which gauge symmetry is spontaneously broken arises in this case

LHC signatures for Z` models with continuously distributed mass

We discuss phenomenological consequences of renormalizable Z` models with continuously distributed mass. We point out that one of possible LHC signatures for such nodel is the existence of broad resonance in Drell-Yan reaction $pp \to Z^{`} \to l^+l^-$.Comment: 7 page

Duality in Off-Shell Electromagnetism

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with Stueckelberg-Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five dimensional theory prevents a natural generalization of the Dirac monopole, since the theory is not symmetric under duality transformations. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles.Comment: 18 page