Articles and Publication Physics Theoretical physics RELATIVISTIC SYMMETRIES OF QUANTUM CHRONODYNAMICS
RELATIVISTIC
SYMMETRIES OF QUANTUM CHRONODYNAMICS
© Oleg Orestovich
Feygin
Northeast Advanced Regional
Projects Agency
Institute of
Scientific & Technological Researches
Ukrainian
Academy of Sciences
Kharkov, Ukraine
Contact to author:
mailto:fond@online.kharkiv.com
http://www.geocites.com/fond_nauka
The logic development of relativistic
principles of quantum chronophysics is
considered based on separate conceptual positions of discrete temporallogy.
Conceptualization's aspects
of relativism in quantum chronodynamic contacts
introduction of temporal frame
of references. Model structurization of relativistic quantum chronodynamic /RQCD/
is accompanied by build-up of group of specific
transformations of symmetry, defining the basic regularities of kinetics of
development of continual - temporal envelopes /CTE/
of physical space. An innovation is temporally
methodology of reviewing traditional quantumtheoretic
representations about existence fundamental CPT -
theorems in a metric Minkowski universe.
In a classical relativistic mechanics, the
particles of a zero mass propellented with a velocity of light are considered.
With the account before entered chronoquantum representations
[1 - 5], a relation features the energy of such particles:
E = p c = p l(h) / h(t), (1)
where p - impulse; c - a velocity of light;
l(h) - Planck length; h(t) - chronoquantum. The ration of two fundamental
stationary values - Planck length and chronoquantum
temporal gap corresponds to a metric velocity of
spatial phase passages - c(h). It naturally defines a upper bound for any
physical velocities of transition of the material plants. It is necessary to
note, that in the formula (1) enough strong assumptions touching an
identification of velocities of distribution of electromagnetic interactions and
metric phase passages are made. Unfortunately, now the shortage of direct
experimental dates does not allow to term other physical processes (for example,
a gravitational interaction), commensurable courses on a velocity with effusive
expansion of the metric of space. Radiating from told,
we shall consider, that the relation (1) in basic is valid for an energy and
impulse of electromagnetic waves. The quantized eigentones of an electromagnetic
field also give a population of its component quantums. One of the basic
relations for quantums of an electromagnetic field is:
h(t) h(e) n ~ m [l(h)
/ h(t)]^2, (2)
where n
- frequency. In chronoquantum's limit from a relation
(2), the analog for one of variants of the known formula of Einstein follows:
m ~ h(e) / c(h)^2. (3)
The formula (3) is valid for in essence
relativistic quantum plants and shows that in an ultrarelativistic case
distinction between a corpuscular substance and a field to become ambiguous.
In a relativistic approximation, the common
chronoquantum mechanical wave
equation maintains the aspect:
i h(e) Δψ[h(t)] = <H[h(t),h(e)]>ψ,
(4)
where <H[h(t), h(e)]> - a fashion of
a chronoquantum mechanical Hamiltonian.
For the equation (4) canonical Lorentz transformation laws, the symmetric
concerning time and coordinates should be valid. Hence, the relativistic
invariance of expression (4) will be defined by a content of a Hamiltonian at
passage from relativistic to a quantum mechanics. To such passage in a
conventional attitude there corresponds input of the chronoquantum
mechanical operational equations:
E => i h(t) h(e) d / dt => i
h(e) Δ[h(t)]; (5)
p = - i h(e) h(t) d / dr => - i
h(e) h(t) Δ[l(h)] => - i h(e) / Δ[c(h)]. (6)
The indicated reasons of symmetry allow receiving
a required Hamiltonian immediately from expression for energy of a quantum
microscopic object:
E = {[c(h) p]^2 + m^2 c(h)^4}^0,5. (7)
The operational sense of the obtained formula (7)
is natural for spotting in view of relations (5) and (6) as:
<H[h(e),h(t)]> = c(h){<a> <p[h(e),h(t)]>}
+ m c(h)^2 <b>; (8)
where <a> and <b> - operators,
the bound with interior symmetries of microscopic objects and operating on their
interior degree of freedoms. Hence, it is possible to count, that exterior
symmetries of quantum plants will be exhausted by symmetries of physical space
and time in the complete correspondence with operational expressions (5), (6)
and (8). Operating functionals <a> and <b> in a traditional quantum
theory contact the interior moment of driving and antimap of a quantum
microsystem. In RQCD, the
sense of an operation of the given operators is supplemented with new degree of
freedoms of localization in CTE. Then the relativistic wave equation for quantum
microscopic objects will have the following discrete shape:
i h(e) Δψ[h(t)] = {c(h){<a> <p[h(e),h(t)]>}
+ m c(h)^2 <b>}ψ. (9)
The equation (9) linearly also satisfies to
one of main principles of a chronoquantum superposition
of states of microscopic objects at localization on next CTE. Temporally
reinterpretation of a psi-function shows [6 - 9], that
for pseudo – Dirac's representation
it is functionally significant, as
ψ = Ψ{ψ[h(t)], ψ[h(e)],
ψ[s(1)], ψ[s(2)], ψ[s(3)]}; (10)
where ψ[s(1)],
ψ[s(2)] and
ψ[s(3)] - components, the bound with a charge,
exterior and interior symmetry of quantum microscopic objects. At the relevant
passage from chronoquantum representation
of the equation of Dirac to a nonrelativistic Schrödinger equations model
representations about ultrarelativistic it is matter - field convergence are
replaced by plans of quantization of fields and annihilation processes.
Major factors, defining world lines of
microscopic objects in RQCD, are multiple acts of localizations on some strictly
sequential population of CTE [10
- 13]. Thus, the unique role will be quite played with various symmetries of
microparticles, in particular antiidentity; the quantum permutable symmetry
linking a spin with a statistician of states and a relativistic kinematic
symmetry, based on Lorentz transformation laws. Classical permutation -
kinematic symmetries represent rotational displacements of the four-dimensional
frame changing a direction of an axis of time in the mathematical ration. In
outcome, there is a gang of the fundamental statements, component a basis of
analog CPT - theorems, defining sequence of
application of operations of a reversion of time T, a specular reflection of
space P and charge conjugation C to the equations of quantum chronodynamic.
In a conventional attitude, completeness of a gang of symmetries reflects
particular physical properties of quantum plant. Therefore, presence of a zero
rest mass reduces in solutions of the equation (9) without P - symmetries. It
can mean that in a passage to the limit: substance
ó field happening
on chronoquantum boundary
of CTE, metric space in representation of Minkowski, will be significally
nonsymmetric.
Explained it is inapplicable to particles
with a nonzero rest mass since in the fixed relative frame of reference all
directions in space are equivalent. It is necessary to note, that here there are
particular didactic inconsistencies between the reference quantum mechanics
referring property P - parities to interior symmetries of microparticles and
RQCD, linking it with properties of metric space. Classical quantumtheoretical
representations contain comparison to exterior
symmetries of the continuous transformations of space and time. Thus discrete
operations P - and T - transformations concern to interior symmetries of quantum
plants. In RQCD, at application CPT - theorems, separation on exterior and
interior symmetries is cleanly the conditional. Basic here is T - transformation,
the bound through temporally variant
CPT - theorems with other symmetries. Thus, traditional separation of symmetries
on exterior - existential and interior - topological
is represented not quite justified.
REFERENCES
1. Feygin O.O. Discrete - temporal model of
Universe // SciTecLibrary (2003). - http://www.sciteclibrary.ru/eng/catalog/pages/5159.html
2. Feygin O.O. Discrete principles of
quantum chronodynamic // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5200.html
3. Feygin O.O. Quantum-theoretical
chrono-discretization // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5201.html
4. Feygin O.O. Cosmological principles of
quantum chronophysics // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5296.html
5. Feygin O.O. Chronodynamic
reinterpretation of Planck’s lengths // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5348.html
6. Feygin O.O. Temporal quantum functionals
// Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5658.html
7. Feygin O.O. Concepts of quantums
chronophysics // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5813.html
8. Feygin O.O. Mechanics of chrono-quantums
// Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5978.html
9. Feygin O.O.
Quantum temporallogy // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/6375.html
10. Feygin O.O. Model
linearization of quantum chronodynamic //
SciTecLibrary (2004). - http://www.sciteclibrary.ru/eng/catalog/pages/7015.html
11. Feygin O.O. Principles
of chronoquantum mechanics // Ibid. – http://www.sciteclibrary.ru/eng/catalog/pages/7016.html
12. Feygin O.O. Elements of relativistic
chronoquantum electrodynamics // Ibid. – http://www.sciteclibrary.ru/eng/catalog/pages/7332.htm
13. Feygin O.O. Gnosiology of discrete
temporalogy // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/7333.htm
Publishing date: May 12, 2004
Source: SciTecLibrary.ru
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