|
Number
|
Articles Title
|
Abstract
|
|
1
|
Liénard-Wiechert
Electromagnetic field
R. Garc?a-Olivo, R. Linares y M., J. L?pez-Bonilla, and A. Rangel-Merino
Full text: Acrobat
PDF (178 KB)
|
The
electromagnetic field generated by a charge in arbitrary motion in
Minkowski space is briefly studied. Particularly important is the deduction
of the superpotential for the radiative part of Maxwell tensor.
|
|
2
|
On Conformal
d'Alembert-Like Equations
E. Capelas de Oliveira and R. da
Rocha
Full text: Acrobat
PDF (125 KB)
|
Using
conformal coordinates associated with projective conformal relativity we
obtain a conformal Klein-Gordon partial differential equation. As a
particular case we present and discuss a conformal `radial' d'Alembert-like
equation. As a by-product we show that this `radial' equation can be
identified with a one-dimensional Schr\"odinger-like equation in which
the potential is exactly the second P\"oschl-Teller potential.
|
|
3
|
Existence of Yang--Mills
Theory with Vacuum Vector and Mass Gap
Igor Hrncic
Full text: Acrobat
PDF (83 KB)
|
This
paper shows that quantum theory describing particles in finite expanding
space--time exhibits natural ultra--violet and infra--red cutoffs as well
as posesses a mass gap and a vacuum vector. Having ultra--violet and
infra--red cutoffs, all renormalization issues disappear. This shows that
Yang--Mills theory exists for any simple compact gauge group and has a mass
gap and a vacuum vector.
|
|
4
|
One-parameter potential from
Darboux Theorem
J Garc?a-Ravelo, J J Pe?a, J Morales, and Shi-Hai Dong
Full text: Acrobat
PDF (128 KB)
|
We
consider the stationary one-dimensional Schr?dinger equation with potential
u(x;i)=\sum\limits_{j=-2}^{2}f_{j}(i)x^{j}, where the coefficients f_{j}(i)
are functions of a discrete parameter i. We establish the most general form
of the coefficients f_{j}(i) and obtain the ladder operators for the
solution of Schr?dinger equation by a Darboux transform. Generally
speaking, the Darboux transform is obtained through a so-called superpotential
W(x), which is derived from a Riccati equation. We first propose a
convenient \textit{ansatz} for the function % W^{\prime }(x) and then yield
a set of nine difference equations for the coefficients f_{j}(i). This set
of difference equations establishes the explicit form of the coefficients f_{j}(i),
in the potential u(x;i). Our results are consistent with some well-known
quantum potentials in special cases.
|
|
5
|
Group Properties of the Black
Scholes Equation and its Solutions
J. P. Singh and S. Prabakaran
Full text: Acrobat
PDF (131 KB)
|
Several
techniques of fundamental physics like quantum mechanics, field theory and
related tools of non-commutative probability, gauge theory, path integral
etc. are being applied for pricing of contemporary financial products and
for explaining various phenomena of financial markets like stock price
patterns, critical crashes etc.. The cardinal contribution of physicists to
the world of finance came from Fischer Black {\&} Myron Scholes through
the option pricing formula which bears their epitaph and which won them the
Nobel Prize for economics in 1997 together with Robert Merton and which
constitutes the cornerstone of contemporary valuation theory. They obtained
closed form expressions for the pricing of financial derivatives by
converting the problem to a heat equation and then solving it for specific
boundary conditions. In this paper, we apply the well-entrenched group theoretic
methods to obtain various solutions of the Black Scholes equation for the
pricing of contingent claims. We also examine the infinitesimal symmetries
of the said equation and explore group transformation properties. The
structure of the Lie algebra of the Black Scholes equation is also studied.
|
|
6
|
Physical Invariants of
Intelligence
Michail Zak
Full text: Acrobat
PDF (218 KB)
|
The
objective of this work is to extend the physical invariants of biosignature
(from disorder to order) to invariants of intelligent behavior: {from
disorder to order via phase transition}. The approach is based upon the
extension of the physics' First Principles that includes behavior of living
systems. The new architecture consists of motor dynamics simulating actual
behavior of the object, and mental dynamics representing evolution of the
corresponding knowledge-base and incorporating it in the form of
information flows into the motor dynamics. Due to feedback from mental
dynamics, the motor dynamics attains quantum-like properties:its trajectory
splits into a family of different trajectories, and each of those
trajectories can be chosen with the probability prescribed by the mental
dynamics. Intelligence is considered as a tool to preserve and improve
survivability of Livings. From the viewpoint of mathematical formalism, it
can be associated with the capability to make decisions that {control} the
motor dynamics via a feedback from the {mental} dynamics by providing a quantum-like
collapse of a random motion into an appropriate deterministic state.
Special attention is focused on data-driven discovery of the underlying
physical model displaying an intelligent behavior within the proposed
formalism.
|
|
7
|
The Numbers Universe: an
outline of the Dirac/Eddington numbers as scaling factors for fractal,
black hole universes
Ross A. McPherson
Full text: Acrobat
PDF (116 KB)
|
The
large number coincidences that fascinated theorists such as Eddington and
Dirac are shown here to be a specific example of a general set of scaling
factors defining universes in which fundamental forces are equated. The
numbers have prescriptive power and they are therefore correct and exact {a
priori}. The universes thus defined exhibit a fractal structure centred on
the Planck/Stoney scale with some formal resemblance to black holes and with
properties analogous to Hawking radiation. The problematic case of emerging
and evaporating universes is briefly considered in the context of quantum
gravity. Historically, the large numbers are associated with the mass of a
charged particle and the mass of the universe. This paper demonstrates that
the numbers are properly understood in the context of four masses including
a non-zero mass derived from Hubble`s Constant and the Planck or Stoney
mass.
|
|
8
|
Quantum Analog of the Black-
Scholes Formula (market of financial derivatives as a continuous fuzzy
measurement
S. I. Melnyk, and I. G.
Tuluzov
Full text: Acrobat
PDF (104 KB)
|
We
analyze the properties of optimum portfolios, the price of which is considered
a new quantum variable and derive a quantum analog of the Black-Scholes
formula for the price of financial variables in assumption that the market
dynamics can by considered as its continuous weak measurement at
no-arbitrage condition.
|
|
9
|
Faster than Light Quantum
Communication
A.Y. Shiekh
Full text: Acrobat
PDF (150 KB)
|
Faster
than light communication might be possible using the collapse of the
quantum wave-function without any accompanying paradoxes.
|
|
10
|
Reply to `On a Recent
Proposal of Faster than Light Quantum Communication'
A.Y. Shiekh
Full text: Acrobat
PDF (105 KB)
|
In a recent paper [1] the author proposed the
possibility of an experiment to perform faster-than-light communication via
the collapse of the quantum wave-function. This was analyzed by Bassi and
Ghirardi [2], and it is believed that this analysis itself merits a
detailed examination.
|
