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

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

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

A Supersymmetric U(1)' Model with Multiple Dark Matters

We consider a scenario where a supersymmetric model has multiple dark matter particles. Adding a U(1)' gauge symmetry is a well-motivated extension of the Minimal Supersymmetric Standard Model (MSSM). It can cure the problems of the MSSM such as the mu-problem or the proton decay problem with high-dimensional lepton number and baryon number violating operators which R-parity allows. An extra parity (U-parity) may arise as a residual discrete symmetry after U(1)' gauge symmetry is spontaneously broken. The Lightest U-parity Particle (LUP) is stable under the new parity becoming a new dark matter candidate. Up to three massive particles can be stable in the presence of the R-parity and the U-parity. We numerically illustrate that multiple stable particles in our model can satisfy both constraints from the relic density and the direct detection, thus providing a specific scenario where a supersymmetric model has well-motivated multiple dark matters consistent with experimental constraints. The scenario provides new possibilities in the present and upcoming dark matter searches in the direct detection and collider experiments.Comment: 25 pages, 5 figure