24,835 research outputs found
Blood oxygen saturation determined by transmission spectrophotometry of hemolyzed blood samples
Use of the Lambert-Beer Transmission Law determines blood oxygen saturation of hemolyzed blood samples. This simplified method is based on the difference in optical absorption properties of hemoglobin and oxyhemoglobin
Gauge Transformations, BRST Cohomology and Wigner's Little Group
We discuss the (dual-)gauge transformations and BRST cohomology for the two
(1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional
(4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries
(and their corresponding generators) for the Lagrangian densities of these
theories. For the 4D free 2-form gauge theory, we show that the changes on the
antisymmetric polarization tensor e^{\mu\nu} (k) due to (i) the (dual-)gauge
transformations corresponding to the internal symmetry group, and (ii) the
translation subgroup T(2) of the Wigner's little group, are connected with
each-other for the specific relationships among the parameters of these
transformation groups. In the language of BRST cohomology defined w.r.t. the
conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states
turn out to be the sum of the original state and the (co-)BRST exact states. We
comment on (i) the quasi-topological nature of the 4D free 2-form gauge theory
from the degrees of freedom count on e^{\mu\nu} (k), and (ii) the Wigner's
little group and the BRST cohomology for the 2D one-form gauge theory {\it
vis-{\`a}-vis} our analysis for the 4D 2-form gauge theory.Comment: LaTeX file, 29 pages, misprints in (3.7), (3.8), (3.9), (3.13) and
(4.14)corrected and communicated to IJMPA as ``Erratum'
Superfield approach to a novel symmetry for non-Abelian gauge theory
In the framework of superfield formalism, we demonstrate the existence of a
new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the
BRST invariant Lagrangian density of a self-interacting two ()-dimensional (2D) non-Abelian gauge theory (having no interaction with
matter fields). The local and nilpotent Noether conserved charges corresponding
to the above continuous symmetries find their geometrical interpretation as the
translation generators along the odd (Grassmannian) directions of the four (-dimensional supermanifold.Comment: LaTeX, 12 pages, equations (4.2)--(4.6) correcte
Equivalent Binary Quadratic Form and the Extended Modular Group
Extended modular group , where
R:z\rightarrow -\bar{z}, \sim
T:z\rightarrow\frac{-1}{z},\simU:z\rightarrow\frac{-1}{z +1} , has been used
to study some properties of the binary quadratic forms whose base points lie in
the point set fundamental region (See \cite{Tekcan1, Flath}).
In this paper we look at how base points have been used in the study of
equivalent binary quadratic forms, and we prove that two positive definite
forms are equivalent if and only if the base point of one form is mapped onto
the base point of the other form under the action of the extended modular group
and any positive definite integral form can be transformed into the reduced
form of the same discriminant under the action of the extended modular group
and extend these results for the subset \QQ^*(\sqrt{-n}) of the imaginary
quadratic field \QQ(\sqrt{-m}).Comment: Paper contains two figures and twelve page
Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism
In the framework of augmented superfield approach, we provide the geometrical
origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST
charges and a non-nilpotent bosonic charge. Together, these local and conserved
charges turn out to be responsible for a clear and cogent definition of the
Hodge decomposition theorem in the quantum Hilbert space of states. The above
charges owe their origin to the de Rham cohomological operators of differential
geometry which are found to be at the heart of some of the key concepts
associated with the interacting gauge theories. For our present review, we
choose the two -dimensional (2D) quantum electrodynamics (QED) as a
prototype field theoretical model to derive all the nilpotent symmetries for
all the fields present in this interacting gauge theory in the framework of
augmented superfield formulation and show that this theory is a {\it unique}
example of an interacting gauge theory which provides a tractable field
theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the
Journal are give
A Concise Introduction to Perturbation Theory in Cosmology
We give a concise, self-contained introduction to perturbation theory in
cosmology at linear and second order, striking a balance between mathematical
rigour and usability. In particular we discuss gauge issues and the active and
passive approach to calculating gauge transformations. We also construct
gauge-invariant variables, including the second order tensor perturbation on
uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected,
reference added, version accepted by CQ
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