57 research outputs found
Gauging gravity with SO(1,3) for spin-1/2 particles
We demonstrate, by analogy with electromagnetism, that the geometric content
in the theory of gravity is an indirect consequence of the fact that the gauge
group in question is the Lorentz group SO(1,3). We hence construct field
equations for gravity and a spin-1/2 particle in a gravitational field based on
gauge considerations. Furthermore, we derive the weak field and Schroedinger
limits of the Dirac equation of the particle in the gravitational field,
especially in Fermi normal coordinates and on the equatorial plane of the Kerr
geometry, following which we identify the terms to which the electromagnetic
potentials A and Phi are analogous.Comment: 21 LaTeX page
IMPACT OF ACTIVE PHARMACEUTICAL INGREDIENT (API) SCARCITY IN PHARMACEUTICAL SECTORS AMIDST COVID-19 PANDEMIC
The novel coronavirus disease 2019 (COVID-19) was characterized as a global pandemic by the World Health Organization (WHO) on March 11, 2020. The present pandemic has caused an intolerable impact on the health structure as well as the pharmaceutical sector, which in ultimatum has created enormous issues in the everyday lives of the patient community. On the other hand, the situation may appear in short and long-term time-horizon and need identification along with appropriate planning to reduce their socio-economic burden. The Indian pharmaceutical industry is the world's third-largest drug producer by volume. India supplies affordable and low-cost generic drugs to millions of people around the globe and operates more than 250 United States Food and Drug Administration (USFDA) and United Kingdom Medicine and Healthcare products Regulatory Agency (UKMHRA) approved plants. Given the Indian pharmaceutical industry, the source of Active Pharmaceutical Ingredients (APIs) for multiple diseases is much crucial part of the Pharma industry’s strategic plan to combat the COVID-19 pandemic. China is the top global producer and exporter of APIs by volume and Indian pharmaceutical industries are also rely heavily on APIs from China for the production of their medicine formulations by importing around 70 percent of the total requirement. However, the present pandemic situation has exposed the world's over-reliance on China in terms of API import and bound world leaders to fig. out sustainable alternatives
Ham Sandwich is Equivalent to Borsuk-Ulam
The Borsuk-Ulam theorem is a fundamental result in algebraic topology, with applications to various areas of Mathematics. A classical application of the Borsuk-Ulam theorem is the Ham Sandwich theorem: The volumes of any n compact sets in R^n can always be simultaneously bisected by an (n-1)-dimensional hyperplane.
In this paper, we demonstrate the equivalence between the Borsuk-Ulam theorem and the Ham Sandwich theorem. The main technical result we show towards establishing the equivalence is the following: For every odd polynomial restricted to the hypersphere f:S^n->R, there exists a compact set A in R^{n+1}, such that for every x in S^n we have f(x)=vol(A cap H^+) - vol(A cap H^-), where H is the oriented hyperplane containing the origin with x as the normal. A noteworthy aspect of the proof of the above result is the use of hyperspherical harmonics.
Finally, using the above result we prove that there exist constants n_0, epsilon_0>0 such that for every n>= n_0 and epsilon <= epsilon_0/sqrt{48n}, any query algorithm to find an epsilon-bisecting (n-1)-dimensional hyperplane of n compact set in [-n^4.51,n^4.51]^n, even with success probability 2^-Omega(n), requires 2^Omega(n) queries
Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes
We construct classes of smooth metrics which interpolate from Bianchi
attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or
geometries in the UV. While we do not obtain these metrics
as solutions of Einstein gravity coupled to a simple matter field theory, we
show that the matter sector stress-energy required to support these geometries
(via the Einstein equations) does satisfy the weak, and therefore also the
null, energy condition. Since Lifshitz or geometries can in
turn be connected to spacetime, our results show that there is no
barrier, at least at the level of the energy conditions, for solutions to arise
connecting these Bianchi attractor geometries to spacetime. The
asymptotic spacetime has no non-normalizable metric deformation turned
on, which suggests that furthermore, the Bianchi attractor geometries can be
the IR geometries dual to field theories living in flat space, with the
breaking of symmetries being either spontaneous or due to sources for other
fields. Finally, we show that for a large class of flows which connect two
Bianchi attractors, a C-function can be defined which is monotonically
decreasing from the UV to the IR as long as the null energy condition is
satisfied. However, except for special examples of Bianchi attractors
(including AdS space), this function does not attain a finite and non-vanishing
constant value at the end points.Comment: 37 pages, 12 figures, The comment regarding the behavior of
C-function for general Bianchi Types appearing in IR or UV clarified, the
relation of Type IX with for made more precise
and a comment regarding type V added in the conclusio
Retarded resonance Casimir-Polder interaction of a uniformly rotating two-atom system
We consider here, a two-atom system is uniformly moving through a circular
ring at an ultra-relativistic speed and weakly interacting with common external
fields. The vacuum fluctuations of the quantum fields generate the entanglement
between the atoms. Hence an effective energy shift is originated, which depends
on the inter-atomic distance. This is commonly known as resonance
Casimir-Polder interaction (RCPI). It is well known that, for a linearly
accelerated system coupled with a massless scalar field, we get a thermal
response when the local inertial approximation is valid. On the contrary, the
non-thermality arises in the presence of the centripetal acceleration. We use
the quantum master equation formalism to calculate the second-order energy
shift of the entangled states in the presence of two kinds of fields. They are
the massive free scalar field and the electromagnetic vector field. For both
cases, we observe the non-thermal behavior. A unique retarded response is also
noticed in comparison to the free massless case, which can be observed via the
polarization transfer technique.Comment: 8 pages, Comments are welcom
A Hyperk\"ahler geometry associated to the BPS structure of the resolved conifold
We associate to the resolved conifold an affine special K\"{a}hler (ASK)
manifold of complex dimension 1, and an instanton corrected hyperk\"{a}hler
(HK) manifold of complex dimension 2. We describe these geometries explicitly,
and show that the instanton corrected HK geometry realizes an Ooguri-Vafa-like
smoothing of the semi-flat HK metric associated to the ASK geometry. On the
other hand, the instanton corrected HK geometry associated to the resolved
conifold can be described in terms of a twistor family of two holomorphic
Darboux coordinates. We study a certain conformal limit of the twistor
coordinates, and conjecture a relation to a solution of a Riemann-Hilbert
problem previously considered by T. Bridgeland.Comment: 49 pages, references added and typos fixed. Previous theorem 43 and
corollary 44 revised, and the rest of the results unchange
- …