150 research outputs found
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
Non-Trivial Ghosts and Second Class Constraints
In a model in which a vector gauge field is coupled to an
antisymmetric tensor field 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 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 and , 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
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
Five-Dimensional Unification of the Cosmological Constant and the Photon Mass
Using a non-Riemannian geometry that is adapted to the 4+1 decomposition of
space-time in Kaluza-Klein theory, the translational part of the connection
form is related to the electromagnetic vector potential and a Stueckelberg
scalar. The consideration of a five-dimensional gravitational action functional
that shares the symmetries of the chosen geometry leads to a unification of the
four-dimensional cosmological term and a mass term for the vector potential.Comment: 8 pages, LaTe
Radiative Properties of the Stueckelberg Mechanism
We examine the mechanism for generating a mass for a U(1) vector field
introduced by Stueckelberg. First, it is shown that renormalization of the
vector mass is identical to the renormalization of the vector field on account
of gauge invariance. We then consider how the vector mass affects the effective
potential in scalar quantum electrodynamics at one-loop order. The possibility
of extending this mechanism to couple, in a gauge invariant way, a charged
vector field to the photon is discussed.Comment: 8 pages, new Introduction, added Reference
LHC discovery potential for models with continuously distributed mass
We study the Large Hadron Collider (LHC) discovery potential for models
with continuously distributed mass for and 14 TeV
centre-of-mass energies. One of possible LHC signatures for such models is the
existence of broad resonance in Drell-Yan reaction .Comment: 14 pages, some references and formula adde
Renormalization Group Functional Equations
Functional conjugation methods are used to analyze the global structure of
various renormalization group trajectories, and to gain insight into the
interplay between continuous and discrete rescaling. With minimal assumptions,
the methods produce continuous flows from step-scaling {\sigma} functions, and
lead to exact functional relations for the local flow {\beta} functions, whose
solutions may have novel, exotic features, including multiple branches. As a
result, fixed points of {\sigma} are sometimes not true fixed points under
continuous changes in scale, and zeroes of {\beta} do not necessarily signal
fixed points of the flow, but instead may only indicate turning points of the
trajectories.Comment: A physical model with a limit cycle added as section IV, along with
reference
Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics
We discuss the application of the method of characteristics to the
renormalization-group equation for the perturbative QCD series within the
electron-positron annihilation cross-section. We demonstrate how one such
renormalization-group improvement of this series is equivalent to a closed-form
summation of the first four towers of renormalization-group accessible
logarithms to all orders of perturbation theory
U(1)' solution to the mu-problem and the proton decay problem in supersymmetry without R-parity
The Minimal Supersymmetric Standard Model (MSSM) is plagued by two major
fine-tuning problems: the mu-problem and the proton decay problem. We present a
simultaneous solution to both problems within the framework of a U(1)'-extended
MSSM (UMSSM), without requiring R-parity conservation. We identify several
classes of phenomenologically viable models and provide specific examples of
U(1)' charge assignments. Our models generically contain either lepton number
violating or baryon number violating renormalizable interactions, whose
coexistence is nevertheless automatically forbidden by the new U(1)' gauge
symmetry. The U(1)' symmetry also prohibits the potentially dangerous and often
ignored higher-dimensional proton decay operators such as QQQL and UUDE which
are still allowed by R-parity. Thus, under minimal assumptions, we show that
once the mu-problem is solved, the proton is sufficiently stable, even in the
presence of a minimum set of exotics fields, as required for anomaly
cancellation. Our models provide impetus for pursuing the collider
phenomenology of R-parity violation within the UMSSM framework.Comment: Version published in Phys. Rev.
Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns
We extend the traditional formulation of Gauge Field Theory by incorporating
the (non-Abelian) gauge group parameters (traditionally simple spectators) as
new dynamical (nonlinear-sigma-model-type) fields. These new fields interact
with the usual Yang-Mills fields through a generalized minimal coupling
prescription, which resembles the so-called Stueckelberg transformation, but
for the non-Abelian case. Here we study the case of internal gauge symmetry
groups, in particular, unitary groups U(N). We show how to couple standard
Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex
projective, Grassman and flag manifolds. These different couplings lead to
distinct (chiral) symmetry breaking patterns and \emph{Higgs-less}
mass-generating mechanisms for Yang-Mills fields.Comment: 11 pages. To appear in Journal of Nonlinear Mathematical Physic
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