73,383 research outputs found

### Supersymmetric Non-local Gas Equation

In this paper we study systematically the question of supersymmetrization of
the non-local gas equation. We obtain both the N=1 and the N=2 supersymmetric
generalizations of the system which are integrable. We show that both the
systems are bi-Hamiltonian. While the N=1 supersymmetrization allows the
hierarchy of equations to be extended to negative orders (local equations), we
argue that this is not the case for the N=2 supersymmetrization. In the bosonic
limit, however, the N=2 system of equations lead to a new coupled integrable
system of equations.Comment: RevTex, 7page

### Discrete phase space - III: The Divergence-free S-matrix elements

In the arena of the discrete phase space and continuous time, the theory of
S-marix is formulated. In the special case of Quantum-Electrodynamics (QED),
the Feynman rules are precisely developed. These rules in the fourmomentum turn
out to be identical to the usual QED, except for the vertex function. The new
vertex function is given by an infinite series which can only be treated in an
asymptotic approximation at the present time. Preliminary approximations prove
that the second order self-energies of a fermion and a photon in the discrete
model have convergent improper integrals. In the final section, a sharper
asymptotic analysis is employed. It is proved that in case the number of
external photon or fermion lines is at least one, then the S-matrix elements
converge in all orders. Moreover, there are no infra-red divergences in this
formulation.Comment: 31 pages, 3 figure

### Discrete phase space - II: The second quantization of free relativistic wave fields

The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are
presented as partial difference equations in the eight-dimensional covariant
discrete phase space. These equations are also furnished as
difference-differential equations in the arena of discrete phase space and
continuous time. The scalar field and electromagnetic fields are quantized with
commutation relations. The spin-1/2 field is quantized with anti-commutation
relations. Moreover, the total momentum, energy and charge of these free
relativisitic quantized fields in the discrete phase space and continuous time
are computed exactly. The results agree completely with those computed from the
relativisitic fields defned on the space-time continuum.Comment: 27 pages, 1 figur

### Spherical Gravitating Systems of Arbitrary Dimension

We study spherically symmetric solutions to the Einstein field equations
under the assumption that the space-time may possess an arbitrary number of
spatial dimensions. The general solution of Synge is extended to describe
systems of any dimension. Arbitrary dimension analogues of known four
dimensional solutions are also presented, derived using the above scheme.
Finally, we discuss the requirements for the existence of Birkhoff's theorems
in space-times of arbitrary dimension with or without matter fields present.
Cases are discussed where the assumptions of the theorem are considerably
weakened yet the theorem still holds. We also discuss where the weakening of
certain conditions may cause the theorem to fail.Comment: 14 pages with one fugure. Uses AMS fonts and Prog. Theor. Phys. style
files. Added section on neutron star and anisotropic fluid star as well as
Comments on Buchdahl's theorem and more analysis regarding the Birkhoff's
theorem. Accepted for publication in Prog. Theor. Phy

### Effective Actions for 0+1 Dimensional Scalar QED and its SUSY Generalization at $T\neq 0$

We compute the effective actions for the 0+1 dimensional scalar field
interacting with an Abelian gauge background, as well as for its supersymmetric
generalization at finite temperature.Comment: 5 pages, Latex fil

### Inhomogeneous cosmologies with tachyonic dust as dark matter

A cosmology is considered driven by a stress-energy tensor consisting of a
perfect fluid, an inhomogeneous pressure term (which we call a ``tachyonic
dust'' for reasons which will become apparent) and a cosmological constant. The
inflationary, radiation dominated and matter dominated eras are investigated in
detail. In all three eras, the tachyonic pressure decreases with increasing
radius of the universe and is thus minimal in the matter dominated era. The
gravitational effects of the dust, however, may still strongly affect the
universe at present time. In case the tachyonic pressure is positive, it
enhances the overall matter {\em density} and is a candidate for dark matter.
In the case where the tachyonic pressure is negative, the recent acceleration
of the universe can be understood without the need for a cosmological constant.
The ordinary matter, however, has positive energy density at all times. In a
later section, the extension to a variable cosmological term is investigated
and a specific model is put forward such that recent acceleration and future
re-collapse is possible.Comment: 23 pages, four figures. Updated version incorporates some changes in
the introduction. Clarification on why the term tachyonic is used. References
added. Accepted for publication in General Relativity and Gravitatio

### Effective actions at finite temperature

This is a more detailed version of our recent paper where we proposed, from
first principles, a direct method for evaluating the exact fermion propagator
in the presence of a general background field at finite temperature. This can,
in turn, be used to determine the finite temperature effective action for the
system. As applications, we discuss the complete one loop finite temperature
effective actions for 0+1 dimensional QED as well as for the Schwinger model in
detail. These effective actions, which are derived in the real time (closed
time path) formalism, generate systematically all the Feynman amplitudes
calculated in thermal perturbation theory and also show that the retarded
(advanced) amplitudes vanish in these theories. Various other aspects of the
problem are also discussed in detail.Comment: 9 pages, revtex, 1 figure, references adde

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