595 research outputs found
The Stueckelberg Field
In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge
theory massive but preserves gauge invariance. The Stueckelberg mechanism is
the introduction of new fields to reveal a symmetry of a gauge--fixed theory.
We first review the Stueckelberg mechanism in the massive Abelian gauge theory.
We then extend this idea to the standard model, stueckelberging the
hypercharge U(1) and thus giving a mass to the physical photon. This introduces
an infrared regulator for the photon in the standard electroweak theory, along
with a modification of the weak mixing angle accompanied by a plethora of new
effects. Notably, neutrinos couple to the photon and charged leptons have also
a pseudo-vector coupling. Finally, we review the historical influence of
Stueckelberg's 1938 idea, which led to applications in many areas not
anticipated by the author, such as strings. We describe the numerous proposals
to generalize the Stueckelberg trick to the non-Abelian case with the aim to
find alternatives to the standard model. Nevertheless, the Higgs mechanism in
spontaneous symmetry breaking remains the only presently known way to give
masses to non-Abelian vector fields in a renormalizable and unitary theory.Comment: 58 pages, revtex4 RMP format. Added references, minor improvements to
tex
Dynamical Lorentz simmetry breaking from 3+1 Axion-Wess-Zumino model
We study the renormalizable abelian vector-field models in the presence of
the Wess-Zumino interaction with the pseudoscalar matter. The renormalizability
is achieved by supplementing the standard kinetic term of vector fields with
higher derivatives. The appearance of fourth power of momentum in the
vector-field propagator leads to the super-renormalizable theory in which the
-function, the vector-field renormalization constant and the anomalous
mass dimension are calculated exactly. It is shown that this model has the
infrared stable fixed point and its low-energy limit is non-trivial. The
modified effective potential for the pseudoscalar matter leads to the possible
occurrence of dynamical breaking of the Lorentz symmetry. This phenomenon is
related to the modification of Electrodynamics by means of the Chern-Simons
(CS) interaction polarized along a constant CS vector. Its presence makes the
vacuum optically active that has been recently estimated from astrophysical
data. We examine two possibilities for the CS vector to be time-like or
space-like, under the assumption that it originates from v.e.v. of some
pseudoscalar matter and show that only the latter one is consistent in the
framework of the AWZ model, because a time-like CS vector makes the vacuum
unstable under pairs creation of tachyonic photon modes with the finite vacuum
decay rate.Comment: 33 pages, no Figures, Plain TeX, submitted to Phys. Rev.
Super-renormalizable or finite completion of the Starobinsky theory
The recent Planck data of Cosmic Microwave Background (CMB) temperature
anisotropies support the Starobinsky theory in which the quadratic Ricci scalar
drives cosmic inflation. We build up a multi-dimensional quantum consisted
ultraviolet completion of the model in a phenomenological "bottom-up approach".
We present the maximal class of theories compatible with unitarity and
(super-)renormalizability or finiteness which reduces to the Starobinsky theory
in the low-energy limit. The outcome is a maximal extension of the
Krasnikov-Tomboulis-Modesto theory including an extra scalar degree of freedom
besides the graviton field. The original theory was afterwards independently
discovered by Biswas-Gerwick-Koivisto-Mazumdar starting from first principles.
We explicitly show power counting super-renormalizability or finiteness (in odd
dimensions) and unitarity (no ghosts) of the theory. Any further extension of
the theory is non-unitary confirming the existence of at most one single extra
degree of freedom, the scalaron. A mechanism to achieve the Starobinsky theory
in string (field) theory is also investigated at the end of the paper.Comment: 12 pages, 1 figur
Gauge theory in deformed N=(1,1) superspace
We review the non-anticommutative Q-deformations of N=(1,1) supersymmetric
theories in four-dimensional Euclidean harmonic superspace. These deformations
preserve chirality and harmonic Grassmann analyticity. The associated field
theories arise as a low-energy limit of string theory in specific backgrounds
and generalize the Moyal-deformed supersymmetric field theories. A
characteristic feature of the Q-deformed theories is the half-breaking of
supersymmetry in the chiral sector of the Euclidean superspace. Our main focus
is on the chiral singlet Q-deformation, which is distinguished by preserving
the SO(4) Spin(4) ``Lorentz'' symmetry and the SU(2) R-symmetry. We present the
superfield and component structures of the deformed N=(1,0) supersymmetric
gauge theory as well as of hypermultiplets coupled to a gauge superfield:
invariant actions, deformed transformation rules, and so on. We discuss quantum
aspects of these models and prove their renormalizability in the abelian case.
For the charged hypermultiplet in an abelian gauge superfield background we
construct the deformed holomorphic effective action.Comment: 1+60 pages, typos corrected, references adde
Electrons in an annealed environment: A special case of the interacting electron problem
The problem of noninteracting electrons in the presence of annealed magnetic
disorder, in addition to nonmagnetic quenched disorder, is considered. It is
shown that the proper physical interpretation of this model is one of electrons
interacting via a potential that is long-ranged in time, and that its technical
analysis by means of renormalization group techniques must also be done in
analogy to the interacting problem. As a result, and contrary to previous
claims, the model does not simply describe a metal-insulator transition in
() dimensions. Rather, it describes a transition
to a ferromagnetic state that, as a function of the disorder, precedes the
metal-insulator transition close to . In , a transition from a
paramagnetic metal to a paramagnetic insulator is possible.Comment: 13 pp., LaTeX, 2 eps figs; final version as publishe
Four-Fermion Theory and the Conformal Bootstrap
We employ the conformal bootstrap to re-examine the problem of finding the
critical behavior of four-Fermion theory at its strong coupling fixed point.
Existence of a solution of the bootstrap equations indicates self-consistency
of the assumption that, in space-time dimensions less than four, the
renormalization group flow of the coupling constant of a four-Fermion
interaction has a nontrivial fixed point which is generally out of the
perturbative regime. We exploit the hypothesis of conformal invariance at this
fixed point to reduce the set of the Schwinger-Dyson bootstrap equations for
four-Fermion theory to three equations which determine the scale dimension of
the Fermion field , the scale dimension of the composite field
and the critical value of the Yukawa coupling constant. We
solve the equations assuming this critical value to be small. We show that this
solution recovers the fixed point for the four-fermion interaction with
-component fermions in the limit of large at (Euclidean) dimensions
between two and four. We perform a detailed analysis of the -expansion in
and demonstrate full agreement with the conformal bootstrap. We argue
that this is a useful starting point for more sophisticated computations of the
critical indices.Comment: 31pp, text and figures both in Latex, UBCTP 92-3
Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory
We discuss the renormalization of a BRST and anti-BRST invariant composite
operator of mass dimension 2 in Yang-Mills theory with the general BRST and
anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this
study stems from a recent claim that the non-vanishing vacuum condensate of the
composite operator in question can be an origin of mass gap and quark
confinement in any manifestly covariant gauge, as proposed by one of the
authors. First, we obtain the renormalization group flow of the Yang-Mills
theory. Next, we show the multiplicative renormalizability of the composite
operator and that the BRST and anti-BRST invariance of the bare composite
operator is preserved under the renormalization. Third, we perform the operator
product expansion of the gluon and ghost propagators and obtain the Wilson
coefficient corresponding to the vacuum condensate of mass dimension 2.
Finally, we discuss the connection of this work with the previous works and
argue the physical implications of the obtained results.Comment: 49 pages, 35 eps-files, A number of typographic errors are corrected.
A paragraph is added in the beginning of section 5.3. Two equations (7.1) and
(7.2) are added. A version to be published in Phys. Rev.
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