23 research outputs found

### Quantum and Classical Phase Space: Separability and Entanglement

The formalism of classical and quantum mechanics on phase space leads to
symplectic and Heisenberg group representations, respectively. The Wigner
functions give a representation of the quantum system using classical
variables. The correspondence between the classical and the quantum criterion
of separability for the system is obtained in terms of these functions.
Entanglement is generic and separability is special. Some applications are
discussed in commonly occuring examples and possibly in exotic systems.Comment: 8 pages, no figure

### Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory

The Ten dimensional Unified field theory has a 4 dimensional Riemannian
spacetime and six dimensional Calabi Yau space structure. The supersymmetric
Yang Mills fields and black holes are solutions in these theories. The
formation of primordial black holes in early universe, the collapse to
singularity of stellar black holes, the Hawking evaporation of microscopic
black holes in LHC are topics of observational and theoretical interest.
The observation of gamma ray bursts and creation of spectrum of particles and
radiation of dark and normal matter occur due to primordial and microscopic
black holes. The approach to singularity in black hole interior solutions,
require the Bogoliubov transforms of SUSY YM fields in black hole geometries;
both during formation and in evaporation. The Hawking effect of radiating black
holes is applicable for all the fields. Invariants can be defined to give the
conditions for these processes.Comment: 8 pages, no figures, [email protected] Physics deptt, St Xavier's
college, Mumbai, India visitor, Institute of mathematical sciences, Chennai,
Indi

### Particle and Field Symmetries and Noncommutative Geometry

The development of Noncommutative Geometry is creating a reworking and new
possibilities in physics. This paper identifies some of the commutation and
derivation structures that arise in particle and field interactions and
fundamental symmetries. The requirements of coexisting structures, and their
consistency, produce a mathematical framework that underlies a fundamental
physics theory. Among other developments in Quantum theory of particles and
fields are the symmetries of gauge fields and the Fermi-Bose symmetry of
particles. These involve a gauge covariant derivation and the action
functionals; and commutation algebras and Bogoliubov transforms. The non
commutative Theta form introduces an additional and fundamental structure. This
paper obtains the interrelations of various structures, and the conditions for
the symmetries of Fermionic/Bosonic particles interacting with Yang Mills gauge
fields. Many example physical systems are being solved, and the mathematical
formalism is being created to understand the fundamental basis of physics.Comment: 9 pages, no figures, [email protected]

### Non commutative quantum spacetime with topological vortex states, and dark matter in the universe

Non commutative geometry is creating new possibilities for physics. Quantum
spacetime geometry and post inflationary models of the universe with matter
creation have an enormous range of scales of time, distance and energy in
between. There is a variety of physics possible till the nucleosynthesis epoch
is reached. The use of topology and non commutative geometry in cosmology is a
recent approach. This paper considers the possibility of topological solutions
of a vortex kind given by non commutative structures. These are interpreted as
dark matter, with the grand unified Yang-Mills field theory energy scale used
to describe its properties. The relation of the model with other existing
theories is discussed.Comment: 7 pages, no figures. [email protected]

### Fundamental Field Theory in Ten Dimensions and The Early Universe

A unified field theory in ten dimensions, of all interactions, can describe
high energy processes occuring in the early universe. In such a theory
transitions that give properties of the universe can occur due to the presence
of algebraic and geometric structures. A correspondence between theory and
observations of the universe is made, to obtain a new interpretation and
properties. This paper consists of a field theory and cosmological model of
dark and normal energy and matter, cosmological constant, acceleration and
inflation in the early universe.Comment: 11 pages,no figures,[email protected]

### Unified Gauge Field Theory and Topological Transitions

The search for a Unified description of all interactions has created many
developments of mathematics and physics. The role of geometric effects in the
Quantum Theory of particles and fields and spacetime has been an active topic
of research. This paper attempts to obtain the conditions for a Unified Gauge
Field Theory, including gravity. In the Yang Mills type of theories with
compactifications from a 10 or 11 dimensional space to a spacetime of 4
dimensions, the Kaluza Klein and the Holonomy approach has been used. In the
compactifications of Calabi Yau spaces and sub manifolds, the Euler number
Topological Index is used to label the allowed states and the transitions. With
a SU(2) or SL(2,C) connection for gravity and the U(1)*SU(2)*SU(3) or SU(5)
gauge connection for the other interactions, a Unified gauge field theory is
expressed in the 10 or 11 dimension space. Partition functions for the sum over
all possible configurations of sub spaces labeled by the Euler number index and
the Action for gauge and matter fields are constructed. Topological Euler
number changing transitions that can occur in the gauge fields and the
compactified spaces, and their significance are discussed. The possible limits
and effects of the physical validity of such a theory are discussed.Comment: 14 pages, no figures, [email protected], (Physics department, St
Xavier's college, Mumbai and visitor, Institute of Mathematical Sciences,
Chennai, India

### Bose Fermi Supersymmetry with Bogoliubov transforms in Cosmology

Field theory including Supersymmetry and Bose Fermi Symmetry is an active
subject of particle physics and cosmology. Recent and expected observational
evidence gives indicators for the creation and destruction of normal and
supersymmetric dark matter in the universe. This paper uses Bogoliubov
transforms in supersymmetric and Bose Fermi form for obtaining the vaccuum
expectation values at any two times in cosmological and black hole geometries.
The isotropic Robertson Walker and slightly anisotropic Bianchi I geometry mode
functions have a differential equation form analogous to the supersymmetric
Hamiltonian. The condition for mixed and distinct representations for bosonic
and fermionic fields of normal and supersymmetric partner particles are found.Comment: 11 pages, no figures. Visitor, Institute of Mathematical Sciences,
Chennai; [email protected]

### Quantisation on general spaces

Quantisation on spaces with properties of curvature, multiple connectedness
and non orientablility is obtained.
The geodesic length spectrum for the Laplacian operator is extended to solve
the Schroedinger operator. Homotopy fundamental group representations are used
to obtain a direct sum of Hilbert spaces, with a Holonomy method for the non
simply connected manifolds.The covering spaces of isometric and hence
isospectral manifolds are used to obtain the representation of states on
orientable and non orientable spaces. Problems of deformations of the operators
and the domains are discussed.Possible applications of the geometric and
topological effects in physics are mentioned.Comment: 7 pages. No figure

### Stability of Thermohaline circulation with respect to fresh water release

The relatively warm climate found in the North- Western Europe is due to the
gulf stream that circulates warm saline water from southern latitudes to
Europe. In North Atlantic ocean the stream gives out a large amount of heat,
cools down and sinks to the bottom to complete the Thermohaline circulation.
There is considerable debate on the stability of the stream to inputs of fresh
water from the melting ice in Greenland and Arctic. The circulation, being
switched off, will have massive impact on the climate of Europe.
Intergovernmental panel on climate change (IPCC) has warned of this danger in
its recent report. Our aim is to model the Thermohaline circulation at the
point where it sinks in the North-Atlantic. We create a two dimensional
discrete map modeling the salinity gradient and vertical velocity of the
stream. We look for how a perturbation in the form of fresh water release can
destabilise the circulation by pushing the velocity below a certain threshold.Comment: Physics department, St Xaviers college, Mumbai and visitor,Institute
of Mathematical sciences, Chenna

### Statistical Physics and Dynamical Systems: Models of Phase Transitions

This paper explores the connection between dynamical system properties and
statistical physics of ensembles of such systems. Simple models are used to
give novel phase transitions; particularly for finite N particle systems with
many physically interesting examples.Comment: 7 pages, no figures, Physics department, St Xavier's college, Mumbai,
India; visitor, Institute of mathematical sciences, Chenna