20 research outputs found
The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case
We study the renormalization of the nonlinear effective SU(2) Lagrangian up
to with spontaneous symmetry breaking. The Stueckelberg
transformation, the background field gauge, the Schwinger proper time and heat
kernel method, and the covariant short distance expansion technology, guarantee
the gauge covariance and incooperate the Ward indentities in our calculations.
The renormalization group equations of the effective couplings are derived and
analyzed. We find that the difference between the results gotten from the
direct method and the renormalization group equation method can be quite large
when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs,
numerical analysis is renew
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
Classical dynamics of a two-species Bose-Einstein condensate in the presence of nonlinear maser processes
The stability analysis of a generalized Dicke model, in the semi-classical
limit, describing the interaction of a two-species Bose-Einstein condensate
driven by a quantized field in the presence of Kerr and spontaneous parametric
processes is presented. The transitions from Rabi to Josephson dynamics are
identified depending on the relative value of the involved parameters.
Symmetry-breaking dynamics are shown for both types of coherent oscillations
due to the quantized field and nonlinear optical processes.Comment: 12 pages, 5 figures. Accepted for publication as chapter in
"Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in
Nonlinear Systems
Deriving Non-decoupling Effects of Heavy Fields from the Path Integral: a Heavy Higgs Field in an SU(2) Gauge Theory
We describe a method to remove non-decoupling heavy fields from a quantized
field theory and to construct a low-energy one-loop effective Lagrangian by
integrating out the heavy degrees of freedom in the path integral. We apply
this method to the Higgs boson in a spontaneously broken SU(2) gauge theory
(gauged linear sigma-model). In this context, the background-field method is
generalized to the non-linear representation of the Higgs sector by applying (a
generalization of) the Stueckelberg formalism. The (background) gauge-invariant
renormalization is discussed. At one loop the log M_H-terms of the heavy-Higgs
limit of this model coincide with the UV-divergent terms of the corresponding
gauged non-linear sigma-model, but vertex functions differ in addition by
finite (constant) terms in both models. These terms are also derived by our
method. Diagrammatic calculations of some vertex functions are presented as
consistency check.Comment: 33 Pages LaTeX, 6 figures uuencoded postscrip
Large-amplitude driving of a superconducting artificial atom: Interferometry, cooling, and amplitude spectroscopy
Superconducting persistent-current qubits are quantum-coherent artificial
atoms with multiple, tunable energy levels. In the presence of large-amplitude
harmonic excitation, the qubit state can be driven through one or more of the
constituent energy-level avoided crossings. The resulting
Landau-Zener-Stueckelberg (LZS) transitions mediate a rich array of
quantum-coherent phenomena. We review here three experimental works based on
LZS transitions: Mach-Zehnder-type interferometry between repeated LZS
transitions, microwave-induced cooling, and amplitude spectroscopy. These
experiments exhibit a remarkable agreement with theory, and are extensible to
other solid-state and atomic qubit modalities. We anticipate they will find
application to qubit state-preparation and control methods for quantum
information science and technology.Comment: 13 pages, 5 figure