Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik

Joos, H.

doi:10.1002/prop.2180100302

Cited by 343 publications

(107 citation statements)

References 44 publications

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“…It should be also noted that according to the Refs. [5][6][7]51,[54][55][56], the basic properties of the Riemann curvature tensor including the relevant results presented in Section 3.6, it would be concluded that the field strength tensor R ρσµν (i.e., the Riemann tensor) the in (1 + 3) space-time dimensions by general covariant massive (tensor) field Equation (71) (formulated solely with a column matrix of the type Ψ R (98-2)), represents a general covariant bispinor field of spin-2 particles (as a generalized massive formulation of the Einstein gravitational field equation). In a similar manner, according to the Refs.…”

Section: Showing That the Universe Could Be Realized Solely By The (1mentioning

confidence: 99%

“…In a similar manner, according to the Refs. [5][6][7]51,[54][55][56], the field strength tensor F µν which is defined in (1 + 3) space-time dimensions by the general covariant massive (tensor) field Equation (72) (formulated solely by a column matrix of the type Ψ F (98-2)), and represents a general covariant bispinor field of spin-1 particles (representing new generalized massive formulations of the Maxwell's equations, and also Yang-Mills field equations). Furthermore, as it would be shown in Section 3.15, the general covariant field Equation (72) (representing the spin-1 boson fields coupling to the spin-1/2 fermionic currents) is also compatible with the SU(2) L ⊗U(2) R and SU(3) symmetry groups.…”

Section: Showing That the Universe Could Be Realized Solely By The (1mentioning

confidence: 99%

“…The extent of their validity is merely the extent to which they correctly predict and agree with experimental results. From a historical point of view, these field equations can be also equivalently written and formulated on the basis of Lagrangian, Hamiltonian, and similar field theoretic formulations in connection with the principle of stationary action [5][6][7][8][9][10].…”

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A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach ‡

Zahedi

2017

Universe

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Abstract:In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Section 2), "it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms." In agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to the fundamental laws of nature is as follows: First, based on the assumption of the rationality of D-momentum and by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras) is derived. Then by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived uniquely as well.Each class of the derived general covariant field equations also includes a definite form of torsion field appearing as the generator of the corresponding field' invariant mass. In addition, it is shown that the (1 + 3)-dimensional cases of two classes of derived field equations represent a new general covariant massive formalism of bispinor fields of spin-2, and spin-1 particles, respectively. In fact, these uniquely determined bispinor fields represent a unique set of new generalized massive forms of the laws governing the fundamental forces of nature, including the Einstein (gravitational), Maxwell (electromagnetic) and Yang-Mills (nuclear) field equations. Moreover, it is also shown that the (1 + 2)-dimensional cases of two classes of these field equations represent (asymptotically) a new general covariant massive formalism of bispinor fields of spin-3/2 and spin-1/2 particles, corresponding to the Dirac and Rarita-Schwinger equations.As a particular consequence, it is shown that a certain massive formalism of general relativity-with a definite form of torsion field appeared originally as the generator of gravitational field's invariant mass-is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that Lagrangian densities specified for the originally derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are also gauge invariant, where the invariant mass of each field ...

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Section: Showing That the Universe Could Be Realized Solely By The (1mentioning

confidence: 99%

Section: Showing That the Universe Could Be Realized Solely By The (1mentioning

confidence: 99%

mentioning

confidence: 99%

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A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach ‡

Zahedi

2017

Universe

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“…The overlap coefficients with the tensor product of single particle states are Poincaré Clebsch-Gordan coefficients which can be found in ( [14][15][3] [16]). …”

Section: The Two-body Problemmentioning

confidence: 99%

Quantitative relativistic effects in the three-nucleon problem

Keister

Polyzou

2006

Phys. Rev. C

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The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincaré invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.

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“…As usual, the theory of RWE closely relates with higher spin formalisms. However, at present there is no a fully adequate formalism for description of higher-spin fields (all widely accepted higher-spin formalisms such as Rarita-Schwinger approach [27], BargmannWigner [5] and Gel'fand-Yaglom [13] multispinor theories, and also Joos-Weinberg 2(2j+1)-component formalism [19,39] have many intrinsic contradictions and difficulties). On the other hand, it is known that the study of RWE leads naturally to the fields which depend on both Minkowski space coordinates and some continuous variables corresponding to spin degrees of freedom [15,5,40,30].…”

Section: Introductionmentioning

confidence: 99%

General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

Варламов

2007

Int J Theor Phys

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A construction of relativistic wave equations on the homogeneous spaces of the Poincaré group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski spacetime and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincaré and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere.

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Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik

Cited by 343 publications

References 44 publications

A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach ‡

A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach ‡

Quantitative relativistic effects in the three-nucleon problem

General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

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