22,500 research outputs found
An integral version of Shor's factoring algorithm
We consider a version of Shor's quantum factoring algorithm such that the
quantum Fourier transform is replaced by an extremely simple one where
decomposition coefficients take only the values of . In numerous
calculations which have been carried out so far, our algorithm has been
surprisingly stable and never failed. There are numerical indications that the
probability of period finding given by the algorithm is a slowly decreasing
function of the number to be factorized and is typically less than in Shor's
algorithm. On the other hand, quantum computer (QC), capable of implementing
our algorithm, will require a much less amount of resources and will be much
less error-sensitive than standard QC. We also propose a modification of
Coppersmith' Approximate Fast Fourier Transform. The numerical results show
that the probability is signifacantly amplified even in the first post integral
approximation. Our algorithm can be very useful at early stages of development
of quantum computer.Comment: LaTex, 27 pages, 2 table
Forms of Relativistic Dynamics, Current Operators and Deep Inelastic Lepton-Nucleon Scattering
The three well-known forms of relativistic dynamics are unitarily equivalent
and the problem of constructing the current operators can be solved in any
form. However the notion of the impulse approximation is reasonable only in the
point form. In particular, the parton model which is the consequence of the
impulse approximation in the front form is incompatible with Lorentz
invariance, P invariance and T invariance. The results for deep inelastic
scattering based on the impulse approximation in the point form give natural
qualitative explanation of the fact that the values given by the parton model
sum rules exceed the corresponding experimental quantities.Comment: 9 pages, LaTe
Fundamental Quantal Paradox and its Resolution
The postulate that coordinate and momentum representations are related to
each other by the Fourier transform has been accepted from the beginning of
quantum theory. As a consequence, coordinate wave functions of photons emitted
by stars have cosmic sizes. This results in a paradox because predictions of
the theory contradict observations. The reason of the paradox and its
resolution are discussed.Comment: 16 pages, no figure
Current Operators in Quantum Field Theory and Sum Rules in Deep Inelastic Scattering
It is shown that in the general case the canonical construction of the
current operators in quantum field theory does not render a bona fide vector
field since Lorentz invariance is violated by Schwinger terms. We argue that
the nonexistence of the canonical current operators for spinor fields follows
from a very simple algebraic consideration. As a result, the well-known sum
rules in deep inelastic scattering are not substantiated.Comment: 18 pages, LaTe
Qualitative Consideration Of The Effect Of Binding In Deep Inelastic Scattering
In our recent paper (hep-ph/9501348) we argued that the Bjorken variable
in deep inelastic scattering cannot be interpreted as the light cone momentum
fraction even in the Bjorken limit and in zero order of the perturbation
theory. The purpose of the present paper is to qualitatively explain this fact
using only a few simplest kinematical relations.Comment: 6 pages, LaTeX
Does The Cosmological Constant Problem Exist?
We first give simple arguments in favor of the "Zero Constants Party", i.e.
that quantum theory should not contain fundamental dimensionful constants at
all. Then we argue that quantum theory should proceed not from a space-time
background but from a Lie algebra, which is treated as a symmetry algebra. With
such a formulation of symmetry, the fact that means not that
the space-time background is curved (since the notion of the space-time
background is not physical) but that the symmetry algebra is the de Sitter
algebra rather than the Poincare one. In particular, there is no need to
involve dark energy or other fields for explaining this fact. As a consequence,
instead of the cosmological constant problem we have a problem why nowadays
Poincare symmetry is so good approximate symmetry. This is rather a problem of
cosmology but not fundamental quantum physics.Comment: 12 pages, no figures, Latex. We give additional arguments that the
cosmological constant problem (which is often called the dark energy problem)
is a purely artificial problem arising as a result of using the notion of
space-time background while this notion is not physical
Finite Mathematics, Finite Quantum Theory And A Conjecture On The Nature Of Time
We first give a rigorous mathematical proof that classical mathematics
(involving such notions as infinitely small/large, continuity etc.) is a
special degenerate case of finite one in the formal limit when the
characteristic of the field or ring in finite mathematics goes to infinity.
We consider a finite quantum theory (FQT) based on finite mathematics and prove
that standard continuous quantum theory is a special case of FQT in the formal
limit . The description of states in standard quantum theory
contains a big redundancy of elements: the theory is based on real numbers
while with any desired accuracy the states can be described by using only
integers, i.e. rational and real numbers play only auxiliary role. Therefore,
in FQT infinities cannot exist in principle, FQT is based on a more fundamental
mathematics than standard quantum theory and the description of states in FQT
is much more thrifty than in standard quantum theory. Space and time are purely
classical notions and are not present in FQT at all. In the present paper we
discuss how classical equations of motions arise as a consequence of the fact
that changes, i.e. is the evolution parameter. It is shown that there
exist scenarios when classical equations of motion for cosmological
acceleration and gravity can be formulated exclusively in terms of quantum
quantities without using space, time and standard semiclassical approximation.Comment: 48 pages, 1 figure. A version published in Physics of Particles and
Nuclei - Springe
Existence of Antiparticles as an Indication of Finiteness of Nature
It is shown that in a quantum theory over a Galois field, the famous Dirac's
result about antiparticles is generalized such that a particle and its
antiparticle are already combined at the level of irreducible representations
of the symmetry algebra without assuming the existence of a local covariant
equation. We argue that the very existence of antiparticles is a strong
indication that nature is described by a finite field rather than by complex
numbers.Comment: 9 pages, Latex. Motivation revisited and considerably shortened.
arXiv admin note: substantial text overlap with arXiv:hep-th/020900
Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry
Physicists usually understand that physics cannot (and should not) derive
that and . At the same time they usually believe that physics should derive the
value of the cosmological constant and that the solution of the dark
energy problem depends on this value. However, background space in General
Relativity (GR) is only a classical notion while on quantum level symmetry is
defined by a Lie algebra of basic operators. We prove that the theory based on
Poincare Lie algebra is a special degenerate case of the theories based on de
Sitter (dS) or anti-de Sitter (AdS) Lie algebras in the formal limit
where R is the parameter of contraction from the latter algebras
to the former one, and has nothing to do with the radius of background
space. As a consequence, is necessarily finite, is fundamental to the same
extent as and , and a question why is as is does not arise.
Following our previous publications, we consider a system of two free bodies in
dS quantum mechanics and show that in semiclassical approximation the
cosmological dS acceleration is necessarily nonzero and is the same as in GR if
the radius of dS space equals and . This result follows from
basic principles of quantum theory. It has nothing to do with existence or
nonexistence of dark energy and therefore for explaining cosmological
acceleration dark energy is not needed. The result is obtained without using
the notion of dS background space (in particular, its metric and connection)
but simply as a consequence of quantum mechanics based on the dS Lie algebra.
Therefore, has a physical meaning only on classical level and the
cosmological constant problem and the dark energy problem do not arise.Comment: 16 pages, no figures. A version published in Physics of Particles and
Nuclei Letters. arXiv admin note: substantial text overlap with
arXiv:1104.4647; text overlap with arXiv:1711.0460
On The Effect of Binding in Deep Inelastic Scattering
The phenomenon of scaling in deep inelastic lepton-nucleon scattering is
usually explained in terms of the Feynman parton model, and the logarithmic
corrections to scaling are explained in the framework of perturbative QCD. For
testing the validity of the parton model, we consider the deep inelastic
electron scattering in a model in which the system electromagnetic current
operator explicitly satisfies relativistic invariance and current conservation.
Let the struck particle have the fraction of the total momentum in the
infinite momentum frame. Then it is shown that, due to binding of particles in
the system under consideration, the Bjorken variable no longer can be
interpreted as , even in the Bjorken limit and in zero order of the
perturbation theory. We argue that, as a result, the data on deep inelastic
scattering alone do not make it possible to determine the distribution of
quarks in the nucleon.Comment: 30 pages, LaTeX
- …