Superalgebraic structure of Lorentz transformations

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Superalgebraic structure of Lorentz transformations. / Monakhov, V. V.

In: Journal of Physics: Conference Series, Vol. 1051, No. 1, 012023, 17.07.2018.

Research output: Contribution to journal › Article › peer-review

Author

Monakhov, V. V. / Superalgebraic structure of Lorentz transformations. In: Journal of Physics: Conference Series. 2018 ; Vol. 1051, No. 1.

BibTeX

@article{ed093258e0194b8d8a70e4ea9fb3d040,

title = "Superalgebraic structure of Lorentz transformations",

abstract = "We constructed superalgebraic representation of the algebra of second quantization of spinors. It is a fermionic analog of the Bargmann-Fock representation and is based on the use of the density of Grassmann variables in impulse space and their derivatives. We showed that Dirac matrices and Lorentz transformation generators can be expressed in terms of such densities. Lorentz transformations are considered as Bogolyubov transformations of creation and annihilation operators. We constructed superalgebraic form of the Dirac equation and the vacuum state vector. We showed that in the superalgebraic form of the complex Clifford algebra generators corresponding to Dirac gamma matrices are not equivalent. Clifford vector corresponding to diagonal matrix γ0 annihilates the vacuum, and the remaining ones give nonzero values. This means that there is asymmetric direction corresponding to the time axis.",

author = "Monakhov, {V. V.}",

year = "2018",

month = jul,

day = "17",

doi = "10.1088/1742-6596/1051/1/012023",

language = "English",

volume = "1051",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

note = "20th International Meeting on Physical Interpretations of Relativity Theory 2017, PIRT 2017 ; Conference date: 03-07-2017 Through 06-07-2017",

}

RIS

TY - JOUR

T1 - Superalgebraic structure of Lorentz transformations

AU - Monakhov, V. V.

PY - 2018/7/17

Y1 - 2018/7/17

N2 - We constructed superalgebraic representation of the algebra of second quantization of spinors. It is a fermionic analog of the Bargmann-Fock representation and is based on the use of the density of Grassmann variables in impulse space and their derivatives. We showed that Dirac matrices and Lorentz transformation generators can be expressed in terms of such densities. Lorentz transformations are considered as Bogolyubov transformations of creation and annihilation operators. We constructed superalgebraic form of the Dirac equation and the vacuum state vector. We showed that in the superalgebraic form of the complex Clifford algebra generators corresponding to Dirac gamma matrices are not equivalent. Clifford vector corresponding to diagonal matrix γ0 annihilates the vacuum, and the remaining ones give nonzero values. This means that there is asymmetric direction corresponding to the time axis.

AB - We constructed superalgebraic representation of the algebra of second quantization of spinors. It is a fermionic analog of the Bargmann-Fock representation and is based on the use of the density of Grassmann variables in impulse space and their derivatives. We showed that Dirac matrices and Lorentz transformation generators can be expressed in terms of such densities. Lorentz transformations are considered as Bogolyubov transformations of creation and annihilation operators. We constructed superalgebraic form of the Dirac equation and the vacuum state vector. We showed that in the superalgebraic form of the complex Clifford algebra generators corresponding to Dirac gamma matrices are not equivalent. Clifford vector corresponding to diagonal matrix γ0 annihilates the vacuum, and the remaining ones give nonzero values. This means that there is asymmetric direction corresponding to the time axis.

UR - http://www.scopus.com/inward/record.url?scp=85051342975&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1051/1/012023

DO - 10.1088/1742-6596/1051/1/012023

M3 - Article

AN - SCOPUS:85051342975

VL - 1051

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012023

T2 - 20th International Meeting on Physical Interpretations of Relativity Theory 2017, PIRT 2017

Y2 - 3 July 2017 through 6 July 2017

ER -

ID: 37031956