“…comme nous l'avons proposé de façon préliminaire dans [Guy 2010c] et [Guy 2010d]. De nombreux auteurs ont constaté le bon, ou meilleur, fonctionnement des équations de la physique en utilisant un paramètre temporel à trois dimensions (par exemple [Demers 1975], [Pappas 1978], [Pappas 1979], [Ziino 1979a], [Ziino 1979b], [Tsabary & Censor 2004], [Chen 2005], [Franco 2006]). Mais ils n'en ont pas compris la véritable portée : le temps n'a pas trois dimensions !…”
Section: Conclusion : Penser Ensemble L'espace Et Le Tempsunclassified
“…comme nous l'avons proposé de façon préliminaire dans [Guy 2010c] et [Guy 2010d]. De nombreux auteurs ont constaté le bon, ou meilleur, fonctionnement des équations de la physique en utilisant un paramètre temporel à trois dimensions (par exemple [Demers 1975], [Pappas 1978], [Pappas 1979], [Ziino 1979a], [Ziino 1979b], [Tsabary & Censor 2004], [Chen 2005], [Franco 2006]). Mais ils n'en ont pas compris la véritable portée : le temps n'a pas trois dimensions !…”
Section: Conclusion : Penser Ensemble L'espace Et Le Tempsunclassified
“…In order to over come the various problems associated with superluminal Lorentz transformations (SLTs), six-dimensional formalism [49][50][51][52][53] of space time is adopted with the symmetric structure of space and time having three space and three time components of a six dimensional space-time. In this formalism, a subluminal observer O in the usual R 4 ≡ ( − → r ,t) space is surrounded by a neighbourhood in which one measures the scalar time |t| ≡ (t 2…”
Section: Bosonic and Fermionic Partners In T 4 -Spacementioning
Constructing the operators connecting the state of energy associated with super partner Hamiltonians and super partner potentials for a linear harmonic oscillator has been discussed and it is shown that any super symmetric eigen state of one of the super partner potentials in T 4 -space is paired in energy with a symmetric eigen state of the other partner potential.
“…In order to over come the various problems associated with superluminal Lorentz transformations (SLTs) [4][5][6][7][8][9][10][11][12][13], six-dimensional formalism [22][23][24][25][26] of space time is adopted with the symmetric structure of space and time having three space and three time components…”
“…No definite answer was known until 1983 when in a largely unnoticed paper, Grenden Shtein [1] pointed out that all these potentials have a property of shape invariance. Keeping in view the recent potential importance of tachyons [2-13] and the fact that these particles are not contradictory to special theory of relativity and are localized in time in view of second quantization and interaction of superluminal electromagnetic fields [14-17], we have constructed a Semi-Unitary Transformation (SUT) to obtain the supersymmetric partner Hamiltonians for one dimensional harmonic oscillator in T 4 -space (i.e the localization space for tachyons [18][19][20][21]) and it has been demonstrated that under this SUT the supersymmetric partner Hamiltonian H T + loses its ground state while its eigen functions constitute a complete orthonormal set in a subspace of full Hilbert space.In order to over come the various problems associated with superluminal Lorentz transformations (SLTs) [4][5][6][7][8][9][10][11][12][13], six-dimensional formalism [22][23][24][25][26] of space time is adopted with the symmetric structure of space and time having three space and three time components
…”
Constructing the Semi-Unitary Transformations (SUT) to obtain the supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator, it has been shown that under this transformation the supersymmetric partner loses its ground state in T 4 -space while its eigen functions constitute a complete orthonormal basis in a subspace of full Hilbert space.
Keywords Supersymmetry · Superluminal Transformations · Semi Unitary TransformationsThere are a number of analytically solvable problems in non-relativistic quantum mechanics for which all the energy eigen values and eigen functions are explicably known. The question naturally arises as to why these potentials are solvable and what is the underlying symmetry property? No definite answer was known until 1983 when in a largely unnoticed paper, Grenden Shtein [1] pointed out that all these potentials have a property of shape invariance. Keeping in view the recent potential importance of tachyons [2-13] and the fact that these particles are not contradictory to special theory of relativity and are localized in time in view of second quantization and interaction of superluminal electromagnetic fields [14-17], we have constructed a Semi-Unitary Transformation (SUT) to obtain the supersymmetric partner Hamiltonians for one dimensional harmonic oscillator in T 4 -space (i.e the localization space for tachyons [18][19][20][21]) and it has been demonstrated that under this SUT the supersymmetric partner Hamiltonian H T + loses its ground state while its eigen functions constitute a complete orthonormal set in a subspace of full Hilbert space.In order to over come the various problems associated with superluminal Lorentz transformations (SLTs) [4][5][6][7][8][9][10][11][12][13], six-dimensional formalism [22][23][24][25][26] of space time is adopted with the symmetric structure of space and time having three space and three time components
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