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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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